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Tangent spaces of a manifold
A tangent bundle is the collection of all of the tangent spaces for all points on a manifold, structured in a way that it forms a new manifold itself.
Tangent_bundle
geometry, the unit tangent bundle of a Riemannian manifold (M, g), denoted by T1M, UT(M), UTM, or SM is the unit sphere bundle for the tangent bundle T(M). It
Unit_tangent_bundle
Continuous surjection satisfying a local triviality condition
unit vectors in E x {\displaystyle E_{x}} . When the vector bundle in question is the tangent bundle T M {\displaystyle TM} , the unit sphere bundle is
Fiber_bundle
Curve whose normals converge asymptotically
the displacement at unit speed along the horocycle tangent to a given unit tangent vector induces a flow on the unit tangent bundle of the hyperbolic plane
Horocycle
Type of Riemannian manifold with constant Jacobi operator spectrum
characteristic polynomial of the Jacobi operator of unit tangent vectors is a constant on the unit tangent bundle. It is named after American mathematician Robert
Osserman_manifold
Bundle of linear subspaces of the tangent bundle
geometry, a contact bundle is a particular type of fiber bundle constructed from a smooth manifold. Like how the tangent bundle is the manifold that
Contact_bundle
Principal fiber bundle
circle bundle. The unit tangent bundle of a non-orientable surface is a circle bundle that is not a principal U ( 1 ) {\displaystyle U(1)} bundle. Only
Circle_bundle
Sphere with radius one, usually centered on the origin of the space
the unit sphere in the dual number plane. Ball n {\displaystyle n} -sphere Sphere Superellipse Unit circle Unit disk Unit tangent bundle Unit square
Unit_sphere
Fiber bundle whose fibers are projective spaces
). The contact bundles, and more generally Grassmann bundles, are projective bundles. The unit tangent bundle of a Riemannian manifold is
Projective_bundle
Straight path on a curved surface or a Riemannian manifold
V is a unit vector, γ V {\displaystyle \gamma _{V}} remains unit speed throughout, so the geodesic flow is tangent to the unit tangent bundle. Liouville's
Geodesic
obtains the Euler–Lagrange equations, which give the geodesic flow on the tangent bundle TM. The geodesic lines are the projections of integral curves of the
Geodesics as Hamiltonian flows
Geodesics_as_Hamiltonian_flows
Colin de Verdière states that a compact Riemannian manifold whose unit tangent bundle is ergodic under the geodesic flow is also ergodic in the sense that
Quantum_ergodicity
Property of measure-preserving dynamical systems
geodesic flow on a Riemannian manifold, usually considered on the unit tangent bundle with its natural invariant measure. On a flat torus, motion in a
Ergodicity
Type of differentiable manifold
{\displaystyle p} . Equivalently, the tangent bundle is a trivial bundle, so that the associated principal bundle of linear frames has a global section
Parallelizable_manifold
System of moving vectors in differential geometry
with an affine connection (a covariant derivative or connection on the tangent bundle), then this connection allows one to transport vectors of the manifold
Parallel_transport
Group of real 2×2 matrices with unit determinant
space, PSL(2, R) can be described as the unit tangent bundle of the hyperbolic plane. It is a circle bundle, and has a natural contact structure induced
SL2(R)
Assignment of a vector to each point in a subset of Euclidean space
setting, a vector field gives a tangent vector at each point of the manifold (that is, a section of the tangent bundle to the manifold). Vector fields
Vector_field
Diffeomorphism that has a hyperbolic structure on the tangent bundle
T^{1}M} be the tangent bundle of unit-length vectors on the manifold M, and let T 1 H {\displaystyle T^{1}H} be the tangent bundle of unit-length vectors
Anosov_diffeomorphism
Branch of geometry
structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a condition called 'complete non-integrability'. Equivalently
Contact_geometry
Fiber bundle whose fibers are group torsors
O(n)} . The example also works for bundles other than the tangent bundle; if E {\displaystyle E} is any vector bundle of rank k {\displaystyle k} over M
Principal_bundle
Vector bundle of rank 1
a line bundle expresses the concept of a line that varies from point to point of a space. For example, a curve in the plane having a tangent line at
Line_bundle
American mathematician (1938–2017)
Kolmogorov. She completed her PhD thesis, titled "Geodesic Flows on Unit Tangent Bundles of Compact Surfaces of Negative Curvature", in 1969. During this
Marina_Ratner
Generalization of Riemannian manifolds
structural equations, except that they are lifted from the manifold to the tangent bundle. However, normal coordinates do not. Every Finsler manifold becomes
Finsler_manifold
positive diagonal matrices and N of lower unitriangular matrices on the unit tangent bundle G / Γ. The Ambrose-Kakutani theorem expresses every ergodic flow
Ergodic_flow
Concept in differential geometry
manifold into a Cartesian product of Riemannian manifolds by splitting the tangent bundle into irreducible spaces under the action of the local holonomy groups
Holonomy
Generalization of an orientation of a vector space
of its tangent bundle. In particular, a differentiable manifold is orientable if and only if its tangent bundle is orientable as a vector bundle. (note:
Orientation of a vector bundle
Orientation_of_a_vector_bundle
Manifold of all orthonormal k-frames in n-dimensional Euclidean space
{\displaystyle V_{2}(\mathbb {R} ^{n})} may be identified with the unit tangent bundle to Sn−1. When k = n or n−1 we saw in the previous section that V
Stiefel_manifold
Concept in mathematics
class of an equivariant vector bundle. The tangent bundle of a manifold or a smooth variety is an equivariant vector bundle. The sheaf of equivariant differential
Equivariant_sheaf
Construct allowing differentiation of tangent vector fields of manifolds
the tangent bundle. A choice of affine connection is also equivalent to a notion of parallel transport, which is a method for transporting tangent vectors
Affine_connection
Mathematical description of mixing substances
Kolmogorov automorphisms, and the Anosov flow (the geodesic flow on the unit tangent bundle of compact manifolds of negative curvature.) The dyadic map is "shift
Mixing_(mathematics)
Differential geometry topic
the set of tangent k-planes in the tangent bundle TM. The target space for the Gauss map N is a Grassmann bundle built on the tangent bundle TM. In the
Gauss_map
Differentiable function whose derivative is everywhere injective
(in terms of the tangent bundle, not stable normal bundle) by Whitney. For example, the Möbius strip has non-trivial tangent bundle, so it cannot immerse
Immersion_(mathematics)
Upper-half plane model of hyperbolic non-Euclidean geometry
{SO}}(2)} . Alternatively, the bundle of unit-length tangent vectors on the upper half-plane, called the unit tangent bundle, is isomorphic to P S L ( 2
Poincaré_half-plane_model
Structure group sub-bundle on a tangent frame bundle
{\displaystyle G} , is a principal G {\displaystyle G} -subbundle of the tangent frame bundle F M {\displaystyle {\text{F}}M} (or GL ( M ) {\displaystyle \operatorname
G-structure_on_a_manifold
Mathematical vector components
parametric curve), then the derivative gives a spanning set for the tangent bundle (it is a basis if and only if the parametrization is an immersion).
Tangential and normal components
Tangential_and_normal_components
Mathematical measure of how much a curve or surface deviates from flatness
the tangent line, or the unit tangent vector, of the curve per unit distance along the curve. Curvature is expressed in units of radians per unit distance
Curvature
Specification of a derivative along a tangent vector of a manifold
mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way
Covariant_derivative
Assignment of a tensor continuously varying across a region of space
(V^{*})^{\otimes q})} where V = T M {\displaystyle V=TM} to be the tangent bundle of M {\displaystyle M} (whose sections are called vector fields or contravariant
Tensor_field
Function in mathematics
defines directional derivative for sections of a vector bundle more general than the tangent bundle. Connections also lead to convenient formulations of
Connection_(mathematics)
Clifford bundle of M is the Clifford bundle generated by the tangent bundle TM. One can also build a Clifford bundle out of the cotangent bundle T*M. The
Clifford_bundle
Affine connection on the tangent bundle of a manifold
the Levi-Civita connection is the unique affine connection on the tangent bundle of a manifold that preserves the (pseudo-)Riemannian metric and is torsion-free
Levi-Civita_connection
Intrinsic geometric structures in mathematics
frame or circle bundles of M. The definitions of the tangent bundle, the unit tangent bundle and the (oriented orthonormal) frame bundle F can be extended
Riemannian connection on a surface
Riemannian_connection_on_a_surface
Infinitesimal version of Lie groupoid
of vector bundles ρ : A → T M {\displaystyle \rho :A\rightarrow TM} , called the anchor, where T M {\displaystyle TM} is the tangent bundle of M {\displaystyle
Lie_algebroid
Structure defining distance on a manifold
Sg defines a section of the bundle Hom(TM, T*M) of vector bundle isomorphisms of the tangent bundle to the cotangent bundle. This section has the same
Metric_tensor
Manifold
– that is, the tangent bundle is equipped with a linear complex structure. Concretely, this is an endomorphism of the tangent bundle whose square is
Complex_manifold
Isomorphism between the tangent and cotangent bundles of a manifold
isomorphism) is an isomorphism between the tangent bundle T M {\displaystyle \mathrm {T} M} and the cotangent bundle T ∗ M {\displaystyle \mathrm {T} ^{*}M}
Musical_isomorphism
d f ) ⊥ {\displaystyle \mathrm {ker} (df)^{\perp }} is a sub-bundle of the tangent bundle of T M {\displaystyle TM} which depends both on the projection
Riemannian_submersion
Quadratic form related to curvatures of surfaces
the second fundamental form (or shape tensor) is a quadratic form on the tangent plane of a smooth surface in the three-dimensional Euclidean space, usually
Second_fundamental_form
Mathematics of smooth surfaces
frame bundle so that its tangent vectors lie in a special subspace of codimension one in the three-dimensional tangent space of the frame bundle. The projection
Differential geometry of surfaces
Differential_geometry_of_surfaces
Line or vector perpendicular to a curve or a surface
curve at a given point is the infinite straight line perpendicular to the tangent line to the curve at the point. A normal vector is a vector perpendicular
Normal_(geometry)
Riemannian manifold with boundary. Suppose that every vector in the unit tangent bundle S M {\displaystyle SM} can be reached via the geodesic flow starting
Santaló's_formula
Canonical differential form
symplectic potential. A similar object is the canonical vector field on the tangent bundle. To define the tautological one-form, select a coordinate chart U {\displaystyle
Tautological_one-form
Graph in economics
the cost-minimizing bundle involves a positive amount of each input, then at a cost-minimizing input bundle an isocost line is tangent to the y-isoquant
Isocost
Generalization of an ordered basis of a vector space
can "solder" a fiber bundle to a smooth manifold, in such a way that the fibers behave as if they were tangent. When the fiber bundle is a homogenous space
Moving_frame
In mathematics, a partition of a manifold into submanifolds
subbundle of the tangent bundle of a manifold) to be tangent to the leaves of a foliation, is that the set of vector fields tangent to the distribution
Foliation
Study of curves from a differential point of view
t0. The first Frenet vector e1(t) is the unit tangent vector in the same direction, called simply the tangent direction, defined at each regular point
Differentiable_curve
Branch of mathematics
differential geometry. A smooth manifold always carries a natural vector bundle, the tangent bundle. Loosely speaking, this structure by itself is sufficient only
Differential_geometry
Map from tangent space to the manifold
well-defined at every point of the tangent bundle. Intuitively speaking, the exponential map takes a given tangent vector to the manifold, runs along
Exponential map (Riemannian geometry)
Exponential_map_(Riemannian_geometry)
Mathematical object
2-sphere, the 3-sphere admits nonvanishing vector fields (sections of its tangent bundle). One can even find three linearly independent and nonvanishing vector
3-sphere
Smooth manifold
J^{2}=-1} when regarded as a vector bundle isomorphism J : T M → T M {\displaystyle J\colon TM\to TM} on the tangent bundle. A manifold equipped with an almost
Almost_complex_manifold
Mathematical concept
G\quad {\mbox{where}}\quad L_{g}(h)=gh,} and this induces a map of the tangent bundle to itself: ( L g ) ∗ : T h G → T g h G . {\displaystyle (L_{g})_{*}:T_{h}G\to
Maurer–Cartan_form
Mathematical measure in Riemannian geometry
manifold M ¯ {\displaystyle {\bar {M}}} , parametrized by arclength, with unit tangent vector T = d γ / d s {\displaystyle T=d\gamma /ds} . Its curvature is
Geodesic_curvature
Natural moving frame in differential geometry of surfaces
(s)=\gamma '(s),} (the unit tangent) u ( s ) = u ( γ ( s ) ) , {\displaystyle \mathbf {u} (s)=\mathbf {u} (\gamma (s)),} (the unit normal) t ( s ) = u
Darboux_frame
Manifold modelled on Hilbert spaces
differentiable. Many basic constructions of manifold theory, such as the tangent space of a manifold and a tubular neighbourhood of a submanifold (of finite
Hilbert_manifold
Smooth manifold with an inner product on each tangent space
Riemannian metric induces an isomorphism of bundles between the tangent bundle and the cotangent bundle. Namely, if g {\displaystyle g} is a Riemannian
Riemannian_manifold
Concept in economics
budget and any two products is tangent to the same indifference curve and this means that every budget line is tangent to, at most, one indifference curve
Indifference_curve
Aspect of economics
the consumption bundle that is on the highest indifference curve that is tangent to B C 1 {\displaystyle BC1} . This consumption bundle is now (X1, Y1)
Consumer_choice
condition that there is a triangle with vertices on the circle and edges tangent to the ellipse. They were introduced by Hartshorne (1978), who showed that
Hartshorne_ellipse
S^{2n-1}} is the form associated to the tangent vector i N → {\displaystyle i{\vec {N}}} , constructed from the unit-normal vector N → {\displaystyle {\vec
Sasakian_manifold
whose local solutions are the geodesics. Geodesic flow is a flow on a tangent bundle TM of a manifold M, generated by a vector field whose trajectories are
Glossary of Riemannian and metric geometry
Glossary_of_Riemannian_and_metric_geometry
Generalization of affine connections
a connection on the frame bundle (principal bundle) of M (or equivalently, a connection on the tangent bundle (vector bundle) of M). A key aspect of the
Cartan_connection
Object in differential geometry
intertwines the right action of GL(n) on the tangent bundle of FM with the adjoint representation on gl(n). The frame bundle also carries a canonical one-form θ
Torsion_tensor
Vector behavior under coordinate changes
covariant indices, because it has parts that live in the tangent bundle as well as the cotangent bundle. A contravariant vector is one which transforms like
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
Algebraic structure in linear algebra
vector bundles provide information about the underlying topological space. For example, the tangent bundle consists of the collection of tangent spaces
Vector_space
Branch of mathematics
application of virtual bundles is with the definition of a virtual tangent bundle of an intersection of spaces: Let Y 1 , Y 2 ⊂ X {\displaystyle Y_{1}
K-theory
Gauge field loop operator
general relativity which compares tangent vectors that live in the tangent spaces at different points. For principal bundles there is a natural way to compare
Wilson_loop
under addition. The tangent bundle of any Lie group can be trivialized via left (or right) multiplication. This means that every tangent space in R {\displaystyle
Darboux_derivative
Microeconomic effect due to a price change
prices, tangent to the "indifference curve"[clarification needed] going through the old bundle, the difference between the new point of tangency and the
Substitution_effect
Symmetry of physical laws under a charge-conjugation transformation
general Riemannian and pseudo-Riemannian manifolds, one has a tangent bundle, a cotangent bundle and a metric that ties the two together. There are several
C-symmetry
Internal groupoid in the category of smooth manifolds
{\displaystyle TG\rightrightarrows TM} , called its tangent groupoid, obtained by considering the tangent bundle of G {\displaystyle G} and M {\displaystyle M}
Lie_groupoid
Differentiable manifold
distribution L, or in other words a complex subbundle of the complexified tangent bundle C T M = T M ⊗ R C {\displaystyle \mathbb {C} TM=TM\otimes _{\mathbb
CR_manifold
Mathematical concept
^{n})=K_{\mathbf {C} }^{0}(\mathbf {CP} ^{n})=\mathbf {Z} [H]/(H-1)^{n+1}.} The tangent bundle satisfies T C P n ⊕ ϑ 1 = H ⊕ n + 1 , {\displaystyle T\mathbf {CP} ^{n}\oplus
Complex_projective_space
Topics referred to by the same term
algebraic analogue Distribution (differential geometry), a subset of the tangent bundle of a manifold Probability distribution, the probability of a particular
Distribution
Combinations of goods and services affordable given income and prices
preferred affordable bundle typically lies at a point where an indifference curve is tangent to the budget line. This tangency point represents the quantities
Budget_constraint
Fundamental formulas linking the metric and curvature tensor of a manifold
in the normal bundle. There are thus a pair of connections: ∇, defined on the tangent bundle of M; and D, defined on the normal bundle of M. These combine
Gauss–Codazzi_equations
Concept in mathematics
4 {\displaystyle \mathbb {HP} ^{1}=S^{4}} , its tangent bundle is stably trivial. The tangent bundles of the rest have nontrivial Stiefel–Whitney and
Quaternionic_projective_space
Concept in consumer economics
bundles of goods X and Y that give a constant utility (points along an indifference curve), the marginal utility of X is measured in terms of units of
Marginal_rate_of_substitution
Topological space associated to a vector bundle
^{-1}(Sq^{i}(\Phi (1)))=\Phi ^{-1}(Sq^{i}(u)).} If we take the bundle in the above to be the tangent bundle of a smooth manifold, the conclusion of the above is
Thom_space
Manifold with Riemannian, complex and symplectic structure
class of the tangent bundle of X {\displaystyle X} in H 2 ( X , R ) {\displaystyle H^{2}(X,\mathbb {R} )} . It follows that the canonical bundle of a compact
Kähler_manifold
equidistant from a center Tangent lines to circles – Line which touches a circle at exactly one point Versor – Quaternion of norm 1 (unit quaternion) Specific
List_of_circle_topics
Problem of allocation of money by consumers in order to most benefit themselves
the utility function should be convex. In this case, optimal bundle lies in the tangency point between the utility function (See Figure 1). 3) Apply the
Utility_maximization_problem
Tensor in differential geometry
(JX,Y)} where J {\displaystyle J} is the complex structure map on the tangent bundle determined by the structure of the Kähler manifold. The Ricci form is
Ricci_curvature
Special functions
first pair of equations states that a and b are tangent at x, the second pair states that a and b are unit vectors, the penultimate equation that a and b
Spin-weighted spherical harmonics
Spin-weighted_spherical_harmonics
Operator generalizing the Laplacian in differential geometry
{\displaystyle \partial _{i}:={\frac {\partial }{\partial x^{i}}}} of the tangent bundle T M {\displaystyle TM} and ∧ {\displaystyle \wedge } is the wedge product
Laplace–Beltrami_operator
Ties Euler characteristic of a closed even-dimensional Riemannian manifold to curvature
the curvature form of any metric connection on the tangent bundle, as well as for other vector bundles over M {\displaystyle M} . Since the dimension is
Chern–Gauss–Bonnet_theorem
principal U(1)-bundle. Furthermore, relative to the standard Riemannian metric on S3, the unit-length vector field along the fibers of the bundle form a Killing
Berger's_sphere
Vector field on a pseudo-Riemannian manifold that preserves the metric tensor
the tangent bundle. After all, fixing any point on a manifold, one can only move in those directions that are tangent. The dimension of the tangent bundle
Killing_vector_field
Expression that may be integrated over a region
fiber at p {\displaystyle p} of the dual bundle of the k {\displaystyle k} th exterior power of the tangent bundle of M {\displaystyle M} . That is, β {\displaystyle
Differential_form
Concept in algebraic geometry
{\displaystyle c_{1}} is the first Chern class of the tangent bundle TX, regarded as a complex vector bundle by choosing any almost complex structure compatible
Quantum_cohomology
Formulation of physics
M} is called the configuration space of the constrained system. Its tangent bundle T M {\displaystyle \displaystyle TM} is called the phase space of the
Newtonian_dynamics
UNIT TANGENT-BUNDLE
UNIT TANGENT-BUNDLE
Boy/Male
Hindu
Knower of virtues, Talented, Excellent, Virtuous
Boy/Male
Indian
Unit of army
Surname or Lastname
English (Suffolk, of Norman origin)
English (Suffolk, of Norman origin) : nickname for someone with silvery hair, a variant of Argent, with the French definite article l(e).French : metonymic occupational name for a silversmith, from French argent ‘silver’.
Male
English
Variant spelling of English Unni, UNI means "afflicted, depressed."
Female
Welsh
Variant spelling of Welsh Enid, ENIT means "soul."
Girl/Female
Hebrew
Graceful.
Surname or Lastname
English
English : variant of Taggart.Possibly an altered spelling of French Target, a nickname for someone who carried a square buckler, Old French targe.
Female
English
English name derived from the vocabulary word, UNITY means "oneness, unity."
Boy/Male
Muslim/Islamic
Unit of army
Surname or Lastname
English
English : from Old French argent ‘silver’, hence probably a nickname for someone with silver-gray hair, or possibly an occupational nickname for a silversmith or moneyer.
Female
Hebrew
(×וּרִית) Hebrew name URIT means "fire, light."
Girl/Female
American, British, English, Irish
Fair
Boy/Male
Hindu
Pure or holy
Boy/Male
Hindu
Joyful unending, Calmness
Girl/Female
Irish English
Together.
Surname or Lastname
English and French
English and French : in medieval times this did not denote a rank in the army, but was an occupational name for a servant, Middle English, Old French sergent (Latin serviens, genitive servientis, present participle of servire ‘to serve’). The surname probably originated for the most part in this sense, but the word also developed various more specialized meanings, being used for example as a technical term for a tenant by military service below the rank of a knight, and as the name for any of certain administrative and legal officials in different localities, which may also have contributed to the development of the surname. The sense ‘non-commissioned officer’ did not arise until the 16th century.William Sargent (1624–1717) came to Gloucester, MA, from Devon, England before 1678. Many of his descendants distinguished themselves in the civil and military affairs of the colonies and some in literary or artistic paths, notably the portrait painter John Singer Sargent (1856–1925).
Girl/Female
Hebrew
Light.
Surname or Lastname
English
English : variant spelling of Tallent or possibly Tallant.
Boy/Male
Indian
Progress
Boy/Male
Muslim
Unit of army
UNIT TANGENT-BUNDLE
UNIT TANGENT-BUNDLE
Female
Welsh
Esperanto name BRAVA means "brave."
Girl/Female
Tamil
Young girl
Boy/Male
Indian
A scholar who wrote about Quran
Girl/Female
Arabic, Muslim
Happy; Honey
Boy/Male
Tamil
Money, Wealth
Boy/Male
Tamil
Venumadhav | வேநà¯à®®à®¾à®¤à®µ
Sum of the Vedas
Girl/Female
Indian
Loving Girl; Diamond
Boy/Male
Hindu
Principal
Girl/Female
Tamil
Kadanmbari | கதாநà¯à®®à¯à®ªà®°à¯€
Female cuckoo, Goddess Saraswati
Boy/Male
Hindu, Indian, Marathi
Omnipresent
UNIT TANGENT-BUNDLE
UNIT TANGENT-BUNDLE
UNIT TANGENT-BUNDLE
UNIT TANGENT-BUNDLE
UNIT TANGENT-BUNDLE
n.
Any one of numerous species of fresh-water mussels belonging to Unio and many allied genera.
n.
Concord; harmony; conjunction; agreement; uniformity; as, a unity of proofs; unity of doctrine.
n.
The number greater by a unit than two; three units or objects.
v. t.
A tangent line curve, or surface; specifically, that portion of the straight line tangent to a curve that is between the point of tangency and a given line, the given line being, for example, the axis of abscissas, or a radius of a circle produced. See Trigonometrical function, under Function.
n.
The quality or state of being tangent; a contact or touching.
n.
The tangent of the complement of an arc or angle. See Illust. of Functions.
a.
meeting a curve or surface at a point and having at that point the same direction as the curve or surface; -- said of a straight line, curve, or surface; as, a line tangent to a curve; a curve tangent to a surface; tangent surfaces.
a.
Rising into a tumor, or a puffy state; swelling; tumid; as, turgent humors.
v. t.
United; joint; as, unite consent.
n.
Tangency.
v. t.
To put together so as to make one; to join, as two or more constituents, to form a whole; to combine; to connect; to join; to cause to adhere; as, to unite bricks by mortar; to unite iron bars by welding; to unite two armies.
v. t.
To unite closely; to knit together.
v. t.
To remove the turns of (a rope or cable) from the bits; as, to unbit a cable.
v. i.
To be united closely; to grow together; as, broken bones will in time knit and become sound.
a.
Having the lips widely separated and gaping like an open mouth; as a ringent bilabiate corolla.
n.
The number greater than eight by a unit; nine units or objects.
a.
Of or pertaining to a unit or units; relating to unity; as, the unitary method in arithmetic.
v. t.
To unite.
v. t.
To unite closely; to connect; to engage; as, hearts knit together in love.
imp. & p. p.
of Knit