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Study of complex manifolds and several complex variables
complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry
Complex_geometry
Branch of mathematics
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is
Geometry
Branch of mathematics
Algebraic geometry occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis
Algebraic_geometry
Overview of and topical guide to geometry
Absolute geometry Affine geometry Algebraic geometry Analytic geometry Birational geometry Complex geometry Computational geometry Conformal geometry Constructive
Outline_of_geometry
Two closely related mathematical subjects
algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with
Algebraic geometry and analytic geometry
Algebraic_geometry_and_analytic_geometry
Branch of mathematics
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.
Differential_geometry
Branch of differential geometry and differential topology
interchangeably with "symplectic geometry". The name "complex group" formerly advocated by me in allusion to line complexes, as these are defined by the vanishing
Symplectic_geometry
Manifold
In differential geometry and complex geometry, a complex manifold or a complex analytic manifold is a manifold with a complex structure, that is an atlas
Complex_manifold
Maths textbook
Geometry of Complex Numbers is an undergraduate textbook on geometry, whose topics include circles, the complex plane, inversive geometry, and non-Euclidean
Geometry_of_Complex_Numbers
Area of mathematics using condensed sets
unify various mathematical subfields, including topology, complex geometry, and algebraic geometry.[citation needed] In particular, Kiran Kedlaya described
Condensed_mathematics
Two geometries based on axioms closely related to those specifying Euclidean geometry
non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the
Non-Euclidean_geometry
Central atom with four substituents located at the corners of a tetrahedron
In a tetrahedral molecular geometry, a central atom is located at the center with four substituents that are located at the corners of a tetrahedron. The
Tetrahedral molecular geometry
Tetrahedral_molecular_geometry
In organometallic chemistry, a "constrained geometry complex" (CGC) is a kind of catalyst used for the production of polyolefins such as polyethylene and
Constrained_geometry_complex
Mathematical concept in algebraic geometry
rational functions on V. In classical algebraic geometry they are ratios of polynomials; in complex geometry these are meromorphic functions and their higher-dimensional
Function field of an algebraic variety
Function_field_of_an_algebraic_variety
Mathematical condition
physics, particularly in the context of electromagnetism and differential geometry, where it relates to the fact that the boundary of a boundary is always
Poincaré_lemma
Type of geometry
projective geometry are simpler statements. For example, the different conic sections are all equivalent in (complex) projective geometry, and some theorems
Projective_geometry
Generalization of a complex manifold that allows the use of singularities
particularly differential geometry and complex geometry, a complex analytic variety or complex analytic space is a generalization of a complex manifold that allows
Complex_analytic_variety
Creating a complex 3D surface or object by combining primitive objects
Constructive solid geometry (CSG; formerly called computational binary solid geometry) is a technique used in solid modeling. Constructive solid geometry allows a
Constructive_solid_geometry
Branch of mathematics studying functions of a complex variable
functions of a complex variable of complex numbers. It is helpful in many branches of mathematics, including functional analysis, algebraic geometry, number
Complex_analysis
Property of a differential manifold that includes complex structures
differential geometry, a generalized complex structure is a property of a differential manifold that includes as special cases a complex structure and
Generalized_complex_structure
Molecular geometry
In chemistry, octahedral molecular geometry, also called square bipyramidal, describes the shape of compounds with six atoms or groups of atoms or ligands
Octahedral_molecular_geometry
Artificial intelligence (AI) program
AlphaGeometry is an artificial intelligence (AI) program that can solve hard problems in Euclidean geometry. The system comprises a data-driven large language
AlphaGeometry
Number with a real and an imaginary part
"Number/Complex Numbers". Analytic continuation Circular motion using complex numbers Complex-base system Complex coordinate space Complex geometry Geometry of
Complex_number
South Korean mathematician (born 1963)
South Korean mathematician, specializing in algebraic geometry and complex differential geometry. Hwang is the eldest son of gayageum musician Hwang Byungki
Jun-Muk_Hwang
Mathematics concept
complex geometry where they play an essential role in the definition of almost complex manifolds, by contrast to complex manifolds. The term "complex
Linear_complex_structure
Manifold with Riemannian, complex and symplectic structure
and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure
Kähler_manifold
Branch of mathematics
of eight possible geometries. 2-dimensional topology can be studied as complex geometry in one variable (Riemann surfaces are complex curves) – by the
Topology
Fundamental operation on complex numbers
descriptions of redirect targets Complex conjugate line – Operation in complex geometry Complex conjugate representation Complex conjugate vector space – Mathematics
Complex_conjugate
In complex geometry, the term positive form refers to several classes of real differential forms of Hodge type (p, p). Real (p,p)-forms on a complex manifold
Positive_form
Russian-French mathematician
his work on these problems.[G86] Later, he applied his methods to complex geometry, proving certain instances of the Oka principle on deformation of continuous
Mikhael Gromov (mathematician)
Mikhael_Gromov_(mathematician)
Study of angle-preserving transformations
In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines
Inversive_geometry
Branch of geometry that studies combinatorial properties and constructive methods
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric
Discrete_geometry
Curve from a cone intersecting a plane
Projective Geometry: A Guided Tour Through Real and Complex Geometry. Springer. ISBN 9783642172854. Samuel, Pierre (1988), Projective Geometry, Undergraduate
Conic_section
Gives general conditions under which sheaf cohomology groups with indices > 0 are zero
Kodaira vanishing theorem is a basic result of complex manifold theory and complex algebraic geometry, describing general conditions under which sheaf
Kodaira_vanishing_theorem
Type of mathematical functions
of algebraic varieties that is study of the algebraic geometry than complex analytic geometry. Many examples of such functions were familiar in nineteenth-century
Function of several complex variables
Function_of_several_complex_variables
Generalization of a polytope in real space
In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real
Complex_polytope
Mathematical concept
discussion). Complex projective space was first introduced by von Staudt (1860) as an instance of what was then known as the "geometry of position",
Complex_projective_space
Mathematical manifold theory
the study of complex projective varieties, is encompassed by the latter case. Hodge theory has become an important tool in algebraic geometry, particularly
Hodge_theory
On the Euler characteristic of a holomorphic vector bundle on a compact complex manifold
Hirzebruch,Topological Methods in Algebraic Geometry ISBN 3-540-58663-6 Huybrechts, Daniel (2004-11-18). Complex geometry: An introduction. Universitext. Springer
Hirzebruch–Riemann–Roch theorem
Hirzebruch–Riemann–Roch_theorem
combustion instability. Although it is much harder to predict, complex grain geometries offer another technique for increasing regression rate and burn
Hybrid_rocket_fuel_regression
Technical drawing of a building or building project
and opening up new possibilities of form using organic shapes and complex geometry. Today, most architectural drawings are created using CAD software
Architectural_drawing
Symbolic and sacred meanings ascribed to certain geometric shapes
Sacred geometry ascribes symbolic and sacred meanings to certain geometric shapes and certain geometric proportions. It is associated with the belief of
Sacred_geometry
Complex convexity is a general term in complex geometry. A set Ω {\displaystyle \Omega } in C n {\displaystyle \mathbb {C} ^{n}} is called C {\displaystyle
Complex_convexity
Italian mathematician (born c.1981)
Mathematical Sciences. Tosatti does research on complex and differential geometry; geometric analysis on complex, Hermitian, and symplectic manifolds; and partial
Valentino_Tosatti
Vietnamese-American mathematician
He is known for his research on complex analysis, partial differential equations, string theory and complex geometry. After graduating from Lycée Jean-Jacques
Duong_Hong_Phong
Mathematics of varieties with integer coordinates
geometry. The extensive development of algebraic geometry in the 20th century produced powerful tools to study these equations. Diophantine geometry is
Diophantine_geometry
Generalizes the Kodaira vanishing theorem for ample vector bundle
In algebraic geometry, Le Potier's vanishing theorem is an extension of the Kodaira vanishing theorem, on vector bundles. The theorem states the following
Le_Potier's_vanishing_theorem
1998 video game
triangular polygons, allowing developers to achieve greater detail and more complex geometry. The game was designed to be more in line with the puzzle-solving gameplay
Tomb_Raider_III
in the field of complex geometry, a holomorphic curve in a complex manifold M is a non-constant holomorphic map f from the complex plane to M. Nevanlinna
Holomorphic_curve
is thus generally synonymous with the complex line, not the complex coordinate plane. Algebraic geometry Complex vector Riemann sphere Brass, Peter; Moser
Complex_line
Pseudometric of complex manifolds
mathematics and especially complex geometry, the Kobayashi metric is a pseudometric intrinsically associated to any complex manifold. It was introduced
Kobayashi_metric
(algebraic geometry) Chow's theorem (algebraic geometry) Cramer's theorem (algebraic curves) (analytic geometry) Hartogs's theorem (complex analysis) Hartogs's
List_of_theorems
Unsolved problem in geometry
unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular complex algebraic variety to its subvarieties
Hodge_conjecture
It is a generalization of the Lie bracket from an operation on the tangent bundle
Today a complex version of the p = 1 {\displaystyle p=1} Courant bracket plays a central role in the field of generalized complex geometry, introduced
Courant_bracket
Model of the extended complex plane plus a point at infinity
geometry, the Riemann sphere is the prototypical example of a Riemann surface, and is one of the simplest complex manifolds. In projective geometry,
Riemann_sphere
American mathematician
the University of Toronto, where he wrote "Representation Theory and Complex Geometry" with Ginzburg. At Toronto, John M. Liew introduced Chriss to "quant"
Neil_Chriss
Operation in complex geometry
In complex geometry, the complex conjugate line of a straight line is the line that it becomes by taking the complex conjugate of each point on this line
Complex_conjugate_line
Indian mathematician and monk of the Ramakrishna Order (born 1968)
best known for his work in hyperbolic geometry, geometric group theory, low-dimensional topology and complex geometry. Mahan Mitra studied at St. Xavier's
Mahan_Mj
Molecular geometry of five coplanar atoms
transition metal complexes. The noble gas compound xenon tetrafluoride adopts this structure as predicted by VSEPR theory. The geometry is prevalent for
Square planar molecular geometry
Square_planar_molecular_geometry
Cohomology theory for complex manifolds
In complex geometry in mathematics, Aeppli cohomology is a cohomology theory for complex manifolds. It serves as a bridge between de Rham cohomology,
Aeppli_cohomology
Mathematics textbook
invariants are based on. A special focus lies on the combination with complex geometry, which includes Kähler manifolds and (stable) holomorphic vector bundles
The Geometry of Four-Manifolds
The_Geometry_of_Four-Manifolds
Point where two or more curves, lines, or edges meet
In geometry, a vertex (pl.: vertices or vertexes), also called a corner, is a point where two or more curves, lines, or line segments meet or intersect
Vertex_(geometry)
of complex analysis are applied to generating functions. Analytic geometry 1. Also known as Cartesian geometry, the study of Euclidean geometry using
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Describes the line bundles on a complex torus or complex abelian variety
mathematics, the Appell–Humbert theorem describes the line bundles on a complex torus or complex abelian variety. It was proved for 2-dimensional tori by Appell (1891)
Appell–Humbert_theorem
Mathematical model of the physical space
Euclidean geometry is a mathematical system attributed to Euclid, an ancient Greek mathematician, which he described in his textbook on geometry, Elements
Euclidean_geometry
Spiral scroll-like ornament that forms the basis of the Ionic order
furniture design, silverware and ceramics. A method of drawing the complex geometry was devised by the ancient Roman architect Vitruvius through the study
Volute
Cohomology theory for complex manifolds
In complex geometry in mathematics, Bott–Chern cohomology is a cohomology theory for complex manifolds. It serves as a bridge between de Rham cohomology
Bott–Chern_cohomology
Mathematical conjecture
In mathematics, specifically in the fields of model theory and complex geometry, Existential Closedness problems aim to determine when systems of equations
Existential closedness conjecture
Existential_closedness_conjecture
Arrangement of steering linkages
The Ackermann steering geometry (also called Ackermann's steering trapezium) is a geometric arrangement of linkages in the steering of a car or other vehicle
Ackermann_steering_geometry
Mathematical model for turbulence
its cost prohibits simulation of practical engineering systems with complex geometry or flow configurations, such as turbulent jets, pumps, vehicles, and
Large_eddy_simulation
American physicist
multiplets and their implications for nonlinear sigma models, generalized complex geometry, and duality in supersymmetric theories. He has also authored more
Sylvester_James_Gates
Chinese mathematician
1965) is a Chinese mathematician, specializing in several complex variables and complex geometry. He is known for his 1998 proof of the "extended future
Xiangyu_Zhou
Swedish mathematician
mathematician. His main contributions concern the theory of several complex variables and complex geometry. He gained in 1971 a BA degree from the University of Gothenburg
Bo_Berndtsson
Theorem in algebraic geometry
In algebraic geometry, the Bogomolov–Sommese vanishing theorem is a result related to the Kodaira–Itaka dimension. It is named after Fedor Bogomolov and
Bogomolov–Sommese vanishing theorem
Bogomolov–Sommese_vanishing_theorem
Theorem in algebraic geometry
PGL2(p) of order p3 − p. One of the fundamental themes in differential geometry is a trichotomy between the Riemannian manifolds of positive, zero, and
Hurwitz's automorphisms theorem
Hurwitz's_automorphisms_theorem
Geometric representation of the complex numbers
and hence “complex planes”. These are the quadratic algebras over the real number field. Complex coordinate space Complex geometry Complex line Constellation
Complex_plane
In mathematics, and especially complex geometry, the holomorphic tangent bundle of a complex manifold M {\displaystyle M} is the holomorphic analogue
Holomorphic_tangent_bundle
Russian American mathematician (born 1957)
Israel Gelfand. Ginzburg wrote a textbook Representation theory and complex geometry with Neil Chriss on geometric representation theory. A paper by Alexander
Victor_Ginzburg
On zeros of derivatives of cubic polynomials
x j + y j i {\displaystyle \zeta _{j}={\frac {b}{a}}x_{j}+y_{j}i} . By geometry of the equilateral triangle, ∑ j ζ j = 0 {\displaystyle \sum _{j}\zeta
Marden's_theorem
The mapping is quite tedious if it involves Complex geometry. In order to model this type of geometry we divide the flow region into various smaller
Grid_classification
Belgian mathematician
He introduced the concept of weights and tested them on objects in complex geometry. He also collaborated with David Mumford on a new description of the
Pierre_Deligne
implement custom models OpenLB supports complex data structures that allow simulations in complex geometries and parallel execution using MPI, OpenMP
OpenLB
Analysis and solving of problems that involve fluid flows
It is currently only used in few specialized codes, which handle complex geometry with high accuracy and efficiency by using embedded boundaries or overlapping
Computational_fluid_dynamics
American mathematician
June 1942) is an American mathematician, specializing in complex geometry and analysis of complex manifolds. Shiffman received in 1964 from Massachusetts
Bernard_Shiffman
Straight figure with zero width and depth
In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature. It is a special case of a curve
Line_(geometry)
Statement in complex analysis
lemma, named after Hermann Amandus Schwarz, is a result in complex differential geometry that estimates the (squared) pointwise norm | ∂ f | 2 {\displaystyle
Schwarz_lemma
Canadian-American mathematician (1925–2020)
partial differential equations and the Newlander–Nirenberg theorem in complex geometry. He is regarded as a foundational figure in the field of geometric
Louis_Nirenberg
Describes when a compact Riemann surface is determined by its Jacobian variety
named after Ruggiero Torelli, is a classical result of algebraic geometry over the complex number field, stating that a non-singular projective algebraic
Torelli_theorem
Topics referred to by the same term
former name of the club's stadium Skoda–El Mir theorem, theorem of complex geometry This disambiguation page lists articles associated with the title Skoda
Skoda
theories of algebraic geometry and complex manifolds. It is named after Takao Fujita, who formulated it in 1985. In complex geometry, the conjecture states
Fujita_conjecture
Manifold with inversion symmetry
spaces appear in the theory of Jordan triple systems, several complex variables, complex geometry, automorphic forms and group representations, in particular
Hermitian_symmetric_space
Generalizes the Kodaira vanishing theorem
4417 [math.CV]. Kobayashi, Shoshichi (2014-07-14). Differential Geometry of Complex Vector Bundles. Princeton University Press. p. 68. ISBN 9781400858682
Nakano_vanishing_theorem
Italian mathematician
Fino is an Italian mathematician specializing in differential geometry, complex geometry, and Lie groups. She is a professor of mathematics in the Giuseppe
Anna_Fino
Russian mathematician (1937–2023)
Gauge field theory and complex geometry. Grundlehren der mathematischen Wissenschaften. Springer. 1988. Cubic forms - algebra, geometry, arithmetics. North
Yuri_Manin
Topics referred to by the same term
bitmap with a transparent background used in 3D graphics to simulate complex geometry All pages with titles beginning with cutout All pages with titles beginning
Cut-out
Castle at Shanghai Disneyland
California, and Shanghai using cloud-based tools to coordinate the castle's complex geometry, structural systems, and themed detailing. Howard Brown, Senior Vice
Enchanted_Storybook_Castle
Parametrizes complex structures on a surface
Gardiner, Frederic P.; Masur, Howard (1991), "Extremal length geometry of Teichmüller space", Complex Variables Theory Appl., 16 (2–3): 209–237, doi:10.1080/17476939108814480
Teichmüller_space
Complex numbers with non-negative imaginary part
geometry, this model is frequently designated the Poincaré half-plane model. Mathematicians sometimes identify the Cartesian plane with the complex plane
Upper_half-plane
French mathematician (1957–2022)
September 1957 – 17 March 2022) was a French mathematician who worked in complex geometry. He was a professor at Université Grenoble Alpes and a permanent member
Jean-Pierre_Demailly
Vietnamese-American computer scientist (born 1982)
2024, Le contributed to the development of AlphaGeometry, an AI system that solves complex geometry problems at a level approaching a human International
Quoc_V._Le
COMPLEX GEOMETRY
COMPLEX GEOMETRY
Surname or Lastname
English
English : habitational name from Coppull in Lancashire, recorded in the 13th century as Cophill, from Old English copp ‘peak’ + hyll ‘hill’.English : nickname from Old French curt peil ‘short hair’.Probably an Americanized spelling of German and Jewish Koppel or German and Dutch Kappel.
Girl/Female
Tamil
Sompurna | ஸோமபà¯à®°à¯à®¨à®¾
Complete
Sompurna | ஸோமபà¯à®°à¯à®¨à®¾
Girl/Female
Hindu, Indian
Complex
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : habitational name from any of various places called Copley, for example in County Durham, Staffordshire, and Yorkshire, from the Old English personal name Coppa (apparently a byname for a tall man) or from copp ‘hilltop’ + lēah ‘woodland clearing’.
Girl/Female
Bengali, Indian
Good Complex
Girl/Female
Arabic, Muslim
Complex; Zigzag; Curling
Girl/Female
Tamil
Complete
Boy/Male
Indian
Complete
Boy/Male
Indian
Complete
Girl/Female
Tamil
Complete
Surname or Lastname
English
English : unexplained.Americanized form of German Koppler.
Girl/Female
Muslim
Complex, Zigzag, Curling
Girl/Female
Tamil
Shesha Harani | ஷேஷ ஹரணீÂ
Complete
Shesha Harani | ஷேஷ ஹரணீÂ
Girl/Female
Tamil
Complete
Boy/Male
Tamil
Complete
Surname or Lastname
English
English : habitational name, probably from Comley in Shropshire or Combley on the Isle of Wight; both are named with Old English cumb ‘valley’ + lēah ‘woodland clearing’.
Boy/Male
Tamil
Complete
Girl/Female
Tamil
Complete
Boy/Male
Tamil
Complete
Boy/Male
Tamil
Poornan | பூரà¯à®¨à®¾à®¨
Complete
COMPLEX GEOMETRY
COMPLEX GEOMETRY
Girl/Female
Arabic, French, Hebrew
Tenderness; Barren
Biblical
to beat with loud strokes
Girl/Female
Italian Russian Spanish American Latin
Brave.
Boy/Male
Arabic, Muslim
Servant of the Fashioner (Allah)
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
River Narmada
Girl/Female
Hindu
Flower
Female
Italian
Italian and Spanish form of French Noëlle, NOELIA means "day of birth."
Girl/Female
Arabic, Hindu, Indian, Muslim
Feminine of Basil
Girl/Female
Tamil
Pavithra | பவிதà¯à®°à®¾Â
Pure
Male
Turkish
Turkish name ILKER means "first man."
COMPLEX GEOMETRY
COMPLEX GEOMETRY
COMPLEX GEOMETRY
COMPLEX GEOMETRY
COMPLEX GEOMETRY
imp. & p. p.
of Couple
a.
Finished; ended; concluded; completed; as, the edifice is complete.
n.
Composed of two or more parts; composite; not simple; as, a complex being; a complex idea.
a.
Intricate; entangled; complicated; complex.
n.
Two taken together; a pair or couple; especially two lines of verse that rhyme with each other.
adv.
In a complex manner; not simply.
n.
One who couples; that which couples, as a link, ring, or shackle, to connect cars.
n.
A complex; an aggregate of parts; a complication.
a.
Not complex; uncompounded; simple.
pl.
of Couple-close
n.
One who compiles; esp., one who makes books by compilation.
a.
One of the pairs of plates of two metals which compose a voltaic battery; -- called a voltaic couple or galvanic couple.
a.
Complex, complicated.
n.
One who complies, yields, or obeys; one of an easy, yielding temper.
a.
Repeatedly compound; made up of complex constituents.
a.
See Couple-close.
imp. & p. p.
of Comply
imp. & p. p.
of Compile
v. t.
To bring to a state in which there is no deficiency; to perfect; to consummate; to accomplish; to fulfill; to finish; as, to complete a task, or a poem; to complete a course of education.
a.
That which joins or links two things together; a bond or tie; a coupler.