翻訳と辞書 Words near each other ・ Hermite normal form ・ Hermite number ・ Hermite polynomials ・ Hermite reciprocity ・ Hermite ring ・ Hermite spline ・ Hermite's cotangent identity ・ Hermite's identity ・ Hermite's problem ・ Hermite–Hadamard inequality ・ Hermite–Minkowski theorem ・ Hermitian adjoint ・ Hermitian connection ・ Hermitian function ・ Hermitian hat wavelet ・ Hermitian manifold ・ Hermitian matrix ・ Hermitian symmetric space ・ Hermitian variety ・ Hermitian wavelet ・ Hermits of Saint William ・ Hermits of St. John the Baptist ・ Hermits of the Most Blessed Virgin Mary of Mount Carmel ・ Hermitude ・ Hermival-les-Vaux ・ Hermle ・ Hermle AG ・ Hermle Clocks ・ Hermleigh Independent School District ・ Hermleigh, Texas Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hermitian manifold ： ウィキペディア英語版 Hermitian manifold In mathematics, a Hermitian manifold is the complex analogue of a Riemannian manifold. Specifically, a Hermitian manifold is a complex manifold with a smoothly varying Hermitian inner product on each (holomorphic) tangent space. One can also define a Hermitian manifold as a real manifold with a Riemannian metric that preserves a complex structure. A complex structure is essentially an almost complex structure with an integrability condition, and this condition yields an unitary structure (U(n) structure) on the manifold. By dropping this condition we get an almost Hermitian manifold. On any almost Hermitian manifold we can introduce a fundamental 2-form, or cosymplectic structure, that depends only on the chosen metric and almost complex structure. This form is always non-degenerate, with the suitable integrability condition (of it also being closed and thus a symplectic form) we get an almost Kähler structure. If both almost complex structure and fundamental form are integrable, we have a Kähler structure. ==Formal definition== A Hermitian metric on a complex vector bundle ''E'' over a smooth manifold ''M'' is a smoothly varying positive-definite Hermitian form on each fiber. Such a metric can be written as a smooth section :$h\; \backslash in\; \backslash Gamma(E\backslash otimes\backslash bar\; E)^$ * such that :$h\_p(\backslash eta,\; \backslash bar\backslash zeta)\; =\; \backslash overline$ for all ζ, η in ''E''''p'' and :$h\_p(\backslash zeta,\backslash bar\backslash zeta)\; >\; 0$ for all nonzero ζ in ''E''''p''. A Hermitian manifold is a complex manifold with a Hermitian metric on its holomorphic tangent space. Likewise, an almost Hermitian manifold is an almost complex manifold with a Hermitian metric on its holomorphic tangent space. On a Hermitian manifold the metric can be written in local holomorphic coordinates (''z''α) as :$h\; =\; h\_\backslash ,dz^\backslash alpha\backslash otimes\; d\backslash bar\; z^\backslash beta$ where $h\_$ are the components of a positive-definite Hermitian matrix. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hermitian manifold」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.