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...

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

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

especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and...

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

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...

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

geometry, a hyperkähler manifold is a Riemannian manifold ( M , g ) {\displaystyle (M,g)} endowed with three integrable almost complex structures I , J , K...

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, a topological space which is a locally Euclidean Hausdorff space Almost complex manifold Algebraic manifold Analytic manifold Calabi–Yau...

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...

structure group (to H {\displaystyle H} ). Several structures on manifolds, such as a complex structure, a symplectic structure, or a Kähler structure, are...

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...

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

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

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

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

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...

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

smooth manifold M {\displaystyle M} , an almost-contact structure consists of a hyperplane distribution Q {\displaystyle Q} , an almost-complex structure...

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

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...

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...

space bundle over the space of maps from a Riemann surface into an almost-complex manifold. The zero set of this section consists of holomorphic maps. If...

In mathematics, a 4-manifold is a 4-dimensional topological manifold. A smooth 4-manifold is a 4-manifold with a smooth structure. In dimension four,...

ideas on that were never widely adopted. Almost complex manifold Complex Poisson manifold Hyper-Kähler manifold Kähler quotient Hyperkähler quotient Kähler–Einstein...

theorem states that a sequence of pseudoholomorphic curves in an almost complex manifold with a uniform energy bound must have a subsequence which limits...

every point of an almost Hermitian manifold and is the reason why every almost complex manifold (in particular every symplectic manifold) has a Spinc structure...

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