• 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...
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  • 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...
    10 KB (1,311 words) - 18:37, 9 September 2024
  • geometry, a Hermitian manifold is the complex analogue of a Riemannian manifold. More precisely, a Hermitian manifold is a complex manifold with a smoothly...
    10 KB (1,548 words) - 19:33, 13 April 2025
  • especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and...
    33 KB (4,739 words) - 20:31, 30 April 2025
  • Thumbnail for Differential geometry
    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}...
    46 KB (5,964 words) - 21:55, 19 May 2025
  • almost complex structure, but this need not be integrable. Symplectic manifolds are special cases of a Poisson manifold. A multisymplectic manifold of...
    23 KB (3,674 words) - 20:57, 8 March 2025
  • geometry, a generalized complex structure is a property of a differential manifold that includes as special cases a complex structure and a symplectic...
    21 KB (3,142 words) - 22:05, 29 April 2025
  • complex geometry where they play an essential role in the definition of almost complex manifolds, by contrast to complex manifolds. The term "complex...
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  • A complex structure may refer to: Almost complex manifold Complex manifold Linear complex structure Generalized complex structure Complex structure deformation...
    370 bytes (65 words) - 22:44, 25 December 2014
  • Topological manifold Almost complex manifold Almost symplectic manifold Calibrated manifold Complex manifold Contact manifold CR manifold Finsler manifold Hermitian...
    4 KB (287 words) - 19:11, 15 September 2022
  • Thumbnail for Manifold
    manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional manifold,...
    68 KB (9,536 words) - 07:03, 23 May 2025
  • 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...
    10 KB (1,493 words) - 23:15, 13 September 2024
  • 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...
    36 KB (5,630 words) - 05:05, 11 March 2025
  • geometry, a hyperkähler manifold is a Riemannian manifold ( M , g ) {\displaystyle (M,g)} endowed with three integrable almost complex structures I , J , K...
    13 KB (1,650 words) - 17:53, 18 March 2025
  • 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...
    42 KB (7,508 words) - 13:07, 21 April 2025
  • Topological manifold, a topological space which is a locally Euclidean Hausdorff space Almost complex manifold Algebraic manifold Analytic manifold Calabi–Yau...
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  • structure group (to H {\displaystyle H} ). Several structures on manifolds, such as a complex structure, a symplectic structure, or a Kähler structure, are...
    20 KB (2,576 words) - 06:58, 26 June 2023
  • Pseudoholomorphic curve (category Complex manifolds)
    J-holomorphic curve) is a smooth map, from a Riemann surface into an almost complex manifold, that satisfies the Cauchy–Riemann equations. Introduced in 1985...
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  • Holomorphic tangent bundle (category Complex manifolds)
    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...
    8 KB (1,456 words) - 21:11, 4 March 2024
  • complex differential form is a differential form on a manifold (usually a complex manifold) which is permitted to have complex coefficients. Complex forms...
    9 KB (1,413 words) - 02:38, 27 April 2024
  • smooth manifold M {\displaystyle M} , an almost-contact structure consists of a hyperplane distribution Q {\displaystyle Q} , an almost-complex structure...
    3 KB (590 words) - 09:06, 27 August 2024
  • structure (or complex spin structure) is a special classifying map that can exist for orientable manifolds. Such manifolds are called spinᶜ manifolds. C stands...
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  • Thumbnail for Charles Ehresmann
    Ehresmann, Charles (1952). "Sur les variétés presques complexes" [On almost complex manifolds]. Proc. Internat. Congr. Math. (in French). 2: 412–419...
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  • Rizza manifold, named after Giovanni Battista Rizza, is an almost complex manifold also supporting a Finsler structure: this kind of manifold is also...
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  • Thumbnail for Heinz Hopf
    1925. In his dissertation, Connections between topology and metric of manifolds (German: Über Zusammenhänge zwischen Topologie und Metrik von Mannigfaltigkeiten)...
    11 KB (970 words) - 05:12, 25 July 2024
  • concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions...
    26 KB (3,677 words) - 14:31, 7 September 2023
  • Shoshichi Kobayashi: "A note on mappings and automorphisms of almost complex manifolds." Annals of Mathematics (1963): 329–334. doi:10.2307/1970219 "A...
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  • Spin structure (redirect from Spin manifold)
    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...
    29 KB (4,373 words) - 01:23, 1 April 2025
  • theorem states that a sequence of pseudoholomorphic curves in an almost complex manifold with a uniform energy bound must have a subsequence which limits...
    2 KB (272 words) - 03:17, 12 April 2025
  • 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...
    11 KB (1,741 words) - 01:37, 15 November 2024