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topology > algebraic topology > manifold > differentiable manifold > Kähler manifold

geometry > topological space > manifold > differentiable manifold > Kähler manifold

geometry > differential geometry > differentiable manifold > Kähler manifold

topology > differential topology > differentiable manifold > Kähler manifold

Preferred term

Kähler manifold

Definition(s)

In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure. The concept was first studied by Jan Arnoldus Schouten and David van Dantzig in 1930, and then introduced by Erich Kähler in 1933. The terminology has been fixed by André Weil. Kähler geometry refers to the study of Kähler manifolds, their geometry and topology, as well as the study of structures and constructions that can be performed on Kähler manifolds, such as the existence of special connections like Hermitian Yang–Mills connections, or special metrics such as Kähler–Einstein metrics.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/K%C3%A4hler_manifold)

Broader concept(s)

differentiable manifold

Narrower concept(s)

In other languages

variété de Kähler

French

URI

http://data.loterre.fr/ark:/67375/PSR-SMMHDXG0-T

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