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Math/physics concept
geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms. Historically
Connection_form
Topics referred to by the same term
Look up connections in Wiktionary, the free dictionary. Connections may refer to: Connection (disambiguation), singular form Connections: An Investigation
Connections
Construct in differenital geometry
In mathematics, a metric connection is a connection in a vector bundle E equipped with a bundle metric; that is, a metric for which the inner product of
Metric_connection
Differential geometry construct on fiber bundles
for an Ehresmann connection is that it can be represented as a differential form, in much the same way as the case of a connection form. If the group acts
Ehresmann_connection
Mechanical connection between two parts
A form-fit, form-locking or form-closed connection is a type of mechanical connection between two parts (such as the head of a screw with a screwdriver)
Form-fit_connection
Construct allowing differentiation of tangent vector fields of manifolds
In differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector
Affine_connection
Function in mathematics
Ehresmann connection Grothendieck connection Levi-Civita connection Connection form Connection (fibred manifold) Connection (principal bundle) Connection (vector
Connection_(mathematics)
Object in differential geometry
manifold M. This principal bundle is equipped with a connection form ω, a gl(n)-valued one-form which maps vertical vectors to the generators of the right
Torsion_tensor
Expression that may be integrated over a region
with a defined connection. The exterior product of a k {\displaystyle k} -form α {\displaystyle \alpha } and an ℓ {\displaystyle \ell } -form β {\displaystyle
Differential_form
Concept in mathematics
{\displaystyle M} . Then a principal G {\displaystyle G} -connection on P {\displaystyle P} is a differential 1-form on P {\displaystyle P} with values in the Lie
Connection_(principal_bundle)
Defines a notion of parallel transport on a bundle
mathematics, and especially differential geometry and gauge theory, a connection on a fiber bundle is a device that defines a notion of parallel transport
Connection_(vector_bundle)
Connection on a spinor bundle
in two common forms: the Levi-Civita spin connection, when it is derived from the Levi-Civita connection, and the affine spin connection, when it is obtained
Spin_connection
Term in differential geometry
In differential geometry, the curvature form describes curvature of a connection on a principal bundle. The Riemann curvature tensor in Riemannian geometry
Curvature_form
Intrinsic geometric structures in mathematics
parallel transport, covariant derivative and connection form. These concepts were put in their current form with principal bundles only in the 1950s. The
Riemannian connection on a surface
Riemannian_connection_on_a_surface
Lie-algebra-valued form is a differential form with values in a Lie algebra. Such forms have important applications in the theory of connections on a principal
Lie algebra–valued differential form
Lie_algebra–valued_differential_form
Generalization of affine connections
connection as a Cartan connection. For Lie groups, Maurer–Cartan frames are used to view the Maurer–Cartan form of the group as a Cartan connection.
Cartan_connection
bundle coordinates (xλ, yi) on Y, an affine connection Γ on Y → X is given by the tangent-valued connection form Γ = d x λ ⊗ ( ∂ λ + Γ λ i ∂ i ) , Γ λ i =
Connection_(affine_bundle)
Concept in differential topology
forms can be viewed as R-valued differential forms. An important case of vector-valued differential forms are Lie algebra-valued forms (a connection form
Vector-valued differential form
Vector-valued_differential_form
Differential form of degree one or section of a cotangent bundle
In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section of
One-form
Affine connection on the tangent bundle of a manifold
Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine connection on the tangent bundle of a manifold that preserves the
Levi-Civita_connection
South Korean rock band
Nerd Connection (Korean: 너드커넥션) is a four-member South Korean rock band. Nerd Connection formed on 31 May 2017, later officially debuting on 12 August
Nerd_Connection
Particular correspondence between two partially ordered sets
theory, a Galois connection is a particular correspondence (typically) between two partially ordered sets (posets). Galois connections find applications
Galois_connection
Regional airline of the United States (1993–2008)
of parent airline BMI. The type of arrangement the C8 code and ATA Connection's form of logo and branding separating the two, has in the past at other
ATA_Connection
Tensor in differential geometry
connection on κ {\displaystyle \kappa } . The curvature of this connection is the 2-form defined by ρ ( X , Y ) = def Ric ( J X , Y ) {\displaystyle \rho
Ricci_curvature
Physical theory with fields invariant under the action of local "gauge" Lie groups
quantity. The curvature form F, a Lie algebra-valued 2-form that is an intrinsic quantity, is constructed from a connection form by F = d A + A ∧ A {\displaystyle
Gauge_theory
structure. This is called the Chern connection on E {\displaystyle E} . The curvature of the Chern connection is a (1, 1)-form. For details, see Hermitian metrics
Hermitian_connection
Mathematics concept
arbitrary connection to turn it into a Levi-Civita connection, i.e. to make a connection be torsionless. Indeed, if one writes θ for the solder form, then
Vertical and horizontal bundles
Vertical_and_horizontal_bundles
Generalization of the Levi-Civita connection
{\displaystyle \alpha _{g}} is a one-form depending on g {\displaystyle g} . If ∇ {\displaystyle \nabla } is a Weyl connection and h = e 2 γ g {\displaystyle
Weyl_connection
Assignment of a tensor continuously varying across a region of space
vector fields and 1-forms simultaneously. A frequent example application of this general rule is showing that the Levi-Civita connection, which is a mapping
Tensor_field
Mathematical concept
single point then the Maurer–Cartan form can also be characterized abstractly as the unique principal connection on the principal bundle G. Indeed, it
Maurer–Cartan_form
Differential form
In mathematics, a volume form or top-dimensional form is a differential form of degree equal to the differentiable manifold dimension. Thus on a manifold
Volume_form
Study of vector bundles, principal bundles, and fibre bundles
P_{U_{\alpha }}} and the connection one-form and curvature can be pulled back along this smooth map. This gives the local connection one-form A α = s α ∗ ν ∈ Ω
Gauge_theory_(mathematics)
Array of numbers describing a metric connection
array of numbers describing a metric connection. The metric connection is a specialization of the affine connection to surfaces or other manifolds endowed
Christoffel_symbols
1975 studio album by Parliament
Mothership Connection is the fourth album by American funk band Parliament, released on December 15, 1975, on Casablanca Records. This concept album is
Mothership_Connection
In conformal differential geometry, a conformal connection is a Cartan connection on an n-dimensional manifold M arising as a deformation of the Klein
Conformal_connection
Italo house group
Black Connection is an Italo house group formed by Corrado Rizza, Gino Woody Bianchi and Dom Scuteri. The group made three singles that charted in the
Black_Connection
Matrix operation which flips a matrix over its diagonal
a bilinear form B : X × X → F, with the relation B(x, y) = u(x)(y). By defining the transpose of this bilinear form as the bilinear form tB defined by
Transpose
Algebraic object with geometric applications
components in a basis related to a particular coordinate system; those components form an array, which can be thought of as a high-dimensional matrix. Tensors have
Tensor
Topological field
which has as "dynamical" fields a 2-form B taking values in the adjoint representation of G, and a connection form A for G. The action is given by S =
BF_model
Exterior algebraic map taking tensors from p forms to n-p forms
follows: d takes a 0-form (a function) to a 1-form, a 1-form to a 2-form, and a 2-form to a 3-form (and takes a 3-form to zero). For a 0-form f = f ( x , y
Hodge_star_operator
Mathematics of smooth surfaces
(1956), the connection 1-form on a surface embedded in Euclidean space E3 is just the pullback under the Gauss map of the connection 1-form on S2. Using
Differential geometry of surfaces
Differential_geometry_of_surfaces
Specification of a derivative along a tangent vector of a manifold
connection Christoffel symbols Connection (algebraic framework) Connection (mathematics) Connection (vector bundle) Connection form Exterior covariant derivative
Covariant_derivative
Link between a client and database server
same machine or not. A connection is required to send commands and receive answers, usually in the form of a result set. Connections are a key concept in
Database_connection
Straight path on a curved surface or a Riemannian manifold
manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization of the notion of a "straight line". The noun geodesic
Geodesic
2001 film by Edward Burns
follows eight cycles in the lives of six Manhattan residents whose inter-connections form a circle that places each of them less than the proverbial six degrees
Sidewalks of New York (2001 film)
Sidewalks_of_New_York_(2001_film)
called the Chern connection. The curvature Θ {\displaystyle \Theta } of the Chern connection is always a purely imaginary (1,1)-form. A line bundle L
Positive_form
Nonprofit advocacy organization
Justice Connection is a nonprofit advocacy organization that supports current and former civil servants at the U.S. Department of Justice (DOJ). Services
Justice_Connection
Partial differential equations whose solutions are instantons
space of the principal bundle. This connection has a curvature form F A {\displaystyle F_{A}} , which is a two-form on X {\displaystyle X} with values
Yang–Mills_equations
American hip hop supergroup
Westside Connection was an American hip-hop supergroup formed by Ice Cube, Mack 10, and WC. The group's debut album, Bow Down, reached the number two position
Westside_Connection
Tensor that describes the 4D geometry of spacetime
there is a unique connection ∇ on any semi-Riemannian manifold that is compatible with the metric and torsion-free. This connection is called the Levi-Civita
Metric tensor (general relativity)
Metric_tensor_(general_relativity)
Algebra associated to any vector space
algebra is affine space. This is also the intimate connection between exterior algebra and differential forms, as to integrate we need a 'differential' object
Exterior_algebra
American psychedelic soul band (1966–74)
Rotary Connection was an American psychedelic soul band, formed in Chicago in 1966. After the band's 1967 debut album Rotary Connection, session musicians
Rotary_Connection
Branch of mathematics
understanding of differential forms, Charles Ehresmann who introduced the theory of fibre bundles and Ehresmann connections, and others. Of particular importance
Differential_geometry
Operation on fibered manifolds
_{i}\,,} which also represents a connection on a fibered manifold. Treating a connection as a vertical-valued form, one comes to the following important
Connection_(fibred_manifold)
The Montclair Connection is a short section of double-track railroad on the NJ Transit Rail Operations system in New Jersey, United States, connecting
Montclair_Connection
Generalization of the Dirac equation
To write down the equation we also need the spin connection, also known as the connection (1-)form. The dual frame fields { e μ } {\displaystyle \{e^{\mu
Dirac equation in curved spacetime
Dirac_equation_in_curved_spacetime
Term in psychology referring to the experience of feeling close and connected to others
Social connection is the experience of feeling close and connected to others. It involves feeling loved, cared for, and valued, and forms the basis of
Social_connection
Type of transport in differential geometry
in defining any Cartan connection is to consider the flat case: in which the connection corresponds to the Maurer-Cartan form on a homogeneous space.
Projective_connection
Notion in geometry
fundamental form in coordinates see List of formulas in Riemannian geometry or Covariant derivative by moving frames see Cartan connection and Curvature form. the
Curvature of Riemannian manifolds
Curvature_of_Riemannian_manifolds
Scalar-valued bilinear function
In mathematics, a bilinear form is a bilinear map V × V → K on a vector space V (the elements of which are called vectors) over a field K (the elements
Bilinear_form
Abstract strategy game subgenre
Schmittberger identified an additional sub-class of connection game in which points were bridged to form connections although the overall goal – forging a path
Connection_game
{\displaystyle \Sigma \to X} . These connections are given by the corresponding tangent-valued connection forms γ = d x λ ⊗ ( ∂ λ + γ λ m ∂ m + γ λ i
Connection_(composite_bundle)
Type of derivative in differential geometry
Generalisations exist for spinor fields, fibre bundles with a connection and vector-valued differential forms. A 'naïve' attempt to define the derivative of a tensor
Lie_derivative
1975 science fiction novel by Alfred Bester
The Computer Connection is a science fiction novel by American writer Alfred Bester. It was originally published as a serial in Analog Science Fiction
The_Computer_Connection
Concept in differential geometry
{\displaystyle \omega } be the connection one-form and ρ ( ω ) {\displaystyle \rho (\omega )} the representation of the connection in g l ( V ) . {\displaystyle
Exterior_covariant_derivative
Tensor index notation for tensor-based calculations
fields on a differentiable manifold, with or without a metric tensor or connection. It is also the modern name for what used to be called the absolute differential
Ricci_calculus
Fungal structure
A clamp connection is a hook-like structure formed by growing hyphal cells of certain fungi. It is a characteristic feature of basidiomycete fungi. It
Clamp_connection
Tensor field in Riemannian geometry
pseudo-Riemannian manifold, or indeed any manifold equipped with an affine connection. It is a central mathematical tool in the theory of general relativity
Riemann_curvature_tensor
Levi-Civita connection parallel transport Development (differential geometry) connection form Cartan connection affine connection conformal connection projective
List of differential geometry topics
List_of_differential_geometry_topics
Theory of gravity
this theory, a spacetime is characterized by a curvature-free linear connection in conjunction with a metric tensor field, both defined in terms of a
Teleparallelism
Connection formed between neurons that allows neurotransmission
In neuroanatomy, a neural pathway is the connection formed by axons that project from neurons to make synapses onto neurons in another location, to enable
Neural_pathway
American Christian movement
The Christian Connection was a Christian movement in the United States of America that developed in several places during the late 18th and early 19th
Christian_Connection
2005 video game
Tamagotchi Connection: Corner Shop is a shop simulator video game developed by NanaOn-Sha and published by Bandai and Atari for the Nintendo DS. Based
Tamagotchi Connection: Corner Shop
Tamagotchi_Connection:_Corner_Shop
Electrical circuit component
of form D and B. Form K contacts (center-off) differ from Form C in that there is a center-off or normally-open position where neither connection is made
Electrical_contact
Electromagnetism in general relativity
the Levi-Civita connection along an infinitesimal closed curve, the curvature of the connection is the holonomy of the U(1)-connection. Electromagnetic
Maxwell's equations in curved spacetime
Maxwell's_equations_in_curved_spacetime
Supercomputer
CM-5s. Connection Machines were noted for their striking visual design. The CM-1 and CM-2 design teams were led by Tamiko Thiel. The physical form of the
Connection_Machine
1989 novella by Saul Bellow
The Bellarosa Connection is a 1989 novella by the American author Saul Bellow. The book takes the form of an ongoing dialogue between the Fonstein family
The_Bellarosa_Connection
Documentary TV series and book by James Burke
Connections is a science education television series created, written, and presented by British science historian James Burke. The series was produced
Connections (British TV series)
Connections_(British_TV_series)
Professional wrestling tag team
1989, but were formally joined as a team in October 1989 to form the Colossal Connection. This was partly done because of André's ailing health, hoping
Colossal_Connection
System of moving vectors in differential geometry
is equipped with an affine connection (a covariant derivative or connection on the tangent bundle), then this connection allows one to transport vectors
Parallel_transport
Mathematical Concept
In mathematics, Voigt notation or Voigt form in multilinear algebra is a way to represent a symmetric tensor by reducing its order. There are a few variants
Voigt_notation
of algae a plug forms, they likely limit the transfer of metabolites between neighbouring cells. Primary pit connections are formed between cells in
Pit_connection
2025 aviation accident in Canada
Delta Connection Flight 4819 was a scheduled international passenger flight from Minneapolis–Saint Paul International Airport in the United States to Toronto
Delta_Connection_Flight_4819
U.S. SEC filing used to register securities involving foreign entities
Form F-4 is an American form used to register securities in connection with business combinations and exchange offers involving foreign private issuers
Form_F-4
curvature 2-form of the connection with the Kähler form is required to be a constant times the identity transformation. Hermitian Yang–Mills connections are special
Hermitian Yang–Mills connection
Hermitian_Yang–Mills_connection
Operation on differential forms
Differential forms and connections, Cambridge, UK: Cambridge University Press, p. 35, ISBN 9780521462594 Flanders, Harley (1989), Differential forms with applications
Exterior_derivative
Dance
connection is physical, non-verbal communication between dancers to facilitate synchronized or coordinated dance movements. Some forms of connection involve
Connection_(dance)
Regional airline brand of the United States
Wikimedia Commons has media related to DeltaConnection. Delta Connection is a brand name under which Delta Air Lines has air service agreements with domestic
Delta_Connection
Covariant derivative of the metric tensor
derivative of the metric tensor. It can be interpreted as the failure of a connection to parallelly transport the metric. Physically, this corresponds to the
Nonmetricity_tensor
Grothendieck connection is a way of viewing connections in terms of descent data from infinitesimal neighbourhoods of the diagonal. The Grothendieck connection is
Grothendieck_connection
Structure group sub-bundle on a tangent frame bundle
bundle of M to an associated vector bundle. Although the solder form is not a connection form, it can sometimes be regarded as a precursor to one. In detail
G-structure_on_a_manifold
Analytic function on the upper half-plane with a certain behavior under the modular group
hint of the connection between modular forms and classical questions in number theory, such as representation of integers by quadratic forms and the partition
Modular_form
Coordinates comprising a distance and an angle
}=rd\theta .} The connection form relative to this frame and the Levi-Civita connection is given by the skew-symmetric matrix of 1-forms ω i j = ( 0 − d
Polar_coordinate_system
Second-rank tensor in quantum chromodynamics
field, a spin-1 gauge field or, in differential-geometric parlance, a connection in the SU(3) principal bundle; A μ {\displaystyle {\mathcal {A}}_{\mu
Gluon_field_strength_tensor
Tensor invariant under permutations of vectors it acts on
manifold ( M , g ) {\displaystyle (M,g)} equipped with its Levi-Civita connection ∇ {\displaystyle \nabla } , the covariant curvature tensor is a symmetric
Symmetric_tensor
Branch of geometry
connection 1-form α {\textstyle \alpha } that satisfies the curvature condition d α = π ∗ ω {\textstyle d\alpha =\pi ^{*}\omega } is a contact form.
Contact_geometry
the Small Form-factor Pluggable transceiver (SFP) interface, but is significantly larger to support 100 Gbit/s. While the electrical connection of a CFP
C_form-factor_pluggable
Type of physical quantity
according to the first definition. The Christoffel symbols of an affine connection on a manifold can be thought of as the correction terms to the partial
Pseudotensor
said to be flat if it is endowed with a linear connection with vanishing curvature, i.e. a flat connection. Let π : E → X {\displaystyle \pi :E\to X} denote
Flat_vector_bundle
Complex-differentiable part of a Maass wave function
theta functions". Zwegers later discovered the connection of the mock theta function with weak Maass forms. Ramanujan associated an order to his mock theta
Mock_modular_form
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