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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Bergman metric ： ウィキペディア英語版 Bergman metric In differential geometry, the Bergman metric is a Hermitian metric that can be defined on certain types of complex manifold. It is so called because it is derived from the Bergman kernel, both of which are named for Stefan Bergman. ==Definition== Let $G\; \backslash subset\; \}^n$ by :$$ g_ (z) := \frac \log K(z,z) , for $z\; \backslash in\; G$. Then the length of a tangent vector $\backslash xi\; \backslash in\; T\_z:=\backslash sqrt(z)\; \backslash xi\_i\; \backslash bar\_j\; \}.$ This metric is called the Bergman metric on ''G''. The length of a (piecewise) ''C''1 curve $\backslash gamma\; \backslash colon\; ()\; \backslash to\; (t)\; \backslash right\backslash vert\_\; dt\; .$ The distance $d\_G(p,q)$ of two points $p,q\; \backslash in\; G$ is then defined as :$$ d_G(p,q):= \inf \\gamma\text\gamma(0)=p\text\gamma(1)=q \} . The distance ''dG'' is called the ''Bergman distance''. The Bergman metric is in fact a positive definite matrix at each point if ''G'' is a bounded domain. More importantly, the distance ''dG'' is invariant under biholomorphic mappings of ''G'' to another domain $G\text{'}$. That is if ''f'' is a biholomorphism of ''G'' and $G\text{'}$, then $d\_G(p,q)\; =\; d\_(f(p),f(q))$. 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「Bergman metric」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.