Almost complex manifold information

mathematics, an almost complex manifold is a smooth manifold equipped with a smooth linear complex structure on each tangent space. Every complex manifold is an...

differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disc in the complex coordinate space C...

geometry, a Hermitian manifold is the complex analogue of a Riemannian manifold. More precisely, a Hermitian manifold is a complex manifold with a smoothly...

^{n}} . Riemannian manifolds with an ω {\displaystyle \omega } -compatible almost complex structure are termed almost-complex manifolds. They generalize...

complex geometry where they play an essential role in the definition of almost complex manifolds, by contrast to complex manifolds. The term "complex...

A complex structure may refer to: Almost complex manifold Complex manifold Linear complex structure Generalized complex structure Complex structure deformation...

from this definition that an almost complex manifold is even-dimensional. An almost complex manifold is called complex if N J = 0 {\displaystyle N_{J}=0}...

Topological manifold Almost complex manifold Almost symplectic manifold Calibrated manifold Complex manifold Contact manifold CR manifold Finsler manifold Hermitian...

cobordism invariants for almost complex manifolds. If M is an almost complex manifold, then its tangent bundle is a complex vector bundle. The Chern classes...

manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional manifold,...

Rizza manifold, named after Giovanni Battista Rizza, is an almost complex manifold also supporting a Finsler structure: this kind of manifold is also...

J-holomorphic curve) is a smooth map from a Riemann surface into an almost complex manifold that satisfies the Cauchy–Riemann equation. Introduced in 1985...

concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions...

complex differential form is a differential form on a manifold (usually a complex manifold) which is permitted to have complex coefficients. Complex forms...

almost complex structures. If the almost complex structures are instead not assumed to be integrable, the manifold is called quaternionic, or almost hypercomplex...

geometry, a generalized complex structure is a property of a differential manifold that includes as special cases a complex structure and a symplectic...

underlying smooth manifold, given the structure of a complex vector space via the almost complex structure J {\displaystyle J} of the complex manifold M {\displaystyle...

Ehresmann, Charles (1952). "Sur les variétés presques complexes" [On almost complex manifolds]. Proc. Internat. Congr. Math. (in French). 2: 412–419...

hypersurface in a complex vector space, or more generally modeled on an edge of a wedge. Formally, a CR manifold is a differentiable manifold M together with...

1925. In his dissertation, Connections between topology and metric of manifolds (German: Über Zusammenhänge zwischen Topologie und Metrik von Mannigfaltigkeiten)...

quaternionic manifold is a quaternionic analog of a complex manifold. The definition is more complicated and technical than the one for complex manifolds due in...

odd). All oriented smooth manifolds of dimension 4 or less are spinC. All almost complex manifolds are spinC. All spin manifolds are spinC. In particle physics...