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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 Geroch's splitting theorem ： ウィキペディア英語版 Geroch's splitting theorem In the theory of causal structure on Lorentzian manifolds, Geroch's theorem or Geroch's splitting theorem (first proved by Robert Geroch) gives a topological characterization of globally hyperbolic spacetimes. ==The theorem== Let $(M,\; g\_)$ be a globally hyperbolic spacetime. Then $(M,\; g\_)$ is strongly causal and there exists a global "time function" on the manifold, i.e. a continuous, surjective map $f:M\; \backslash rightarrow\; \backslash mathbb$ such that: *For all $t\; \backslash in\; \backslash mathbb$, $f^(t)$ is a Cauchy surface, and *$f$ is strictly increasing on any causal curve. Moreover, all Cauchy surfaces are homeomorphic, and $M$ is homeomorphic to $S\; \backslash times\; \backslash mathbb$ where $S$ is any Cauchy surface of $M$. 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「Geroch's splitting theorem」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.