翻訳と辞書 Words near each other ・ Raubal ・ Rauberflaket ・ Raubling ・ Raubold House ・ Raubritter ・ Raubsville, Pennsylvania ・ Raubtier ・ Raucaffricine beta-glucosidase ・ Raucaffrinoline ・ Rauceby ・ Rauceby Hospital ・ Rauceby railway station ・ Rauch ・ Rauch (company) ・ Rauch and Lang ・ Rauch comparison theorem ・ Rauch House ・ Rauch Partido ・ Rauch, Buenos Aires ・ Rauch, Minnesota ・ Rauch-Haus-Song ・ Raucheck ・ Rauchen und Yoga ・ Rauchenwarth ・ Rauchkofel ・ Rauchkofel Formation ・ Rauchkäse ・ Rauchtown ・ Rauchtown Run ・ Rauchtown, Pennsylvania 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 Rauch comparison theorem ： ウィキペディア英語版 Rauch comparison theorem In Riemannian geometry, the Rauch comparison theorem, named after Harry Rauch who proved it in 1951, is a fundamental result which relates the sectional curvature of a Riemannian manifold to the rate at which geodesics spread apart. Intuitively, it states that for positive curvature, geodesics tend to converge, while for negative curvature, geodesics tend to spread. This theorem is formulated using Jacobi fields to measure the variation in geodesics. ==Statement of the Theorem== Let $M,\; \backslash widetilde$ be Riemannian manifolds, let $\backslash gamma\; :\; (T)\; \backslash to\; M$ and $\backslash widetilde\; :\; ()\; \backslash to\; \backslash widetilde$ be unit speed geodesic segments such that $\backslash widetilde(0)$ has no conjugate points along $\backslash widetilde$, and let $J,\; \backslash widetilde$ be normal Jacobi fields along $\backslash gamma$ and $\backslash widetilde$ such that $J(0)\; =\; \backslash widetilde(0)\; =\; 0$ and $|D\_t\; J(0)|\; =\; |\backslash widetilde\_t\; \backslash widetilde(0)|$. Suppose that the sectional curvatures of $M$ and $\backslash widetilde$ satisfy $K(\backslash Pi)\; \backslash leq\; \backslash widetilde(\backslash widetilde)$ whenever $\backslash Pi\; \backslash subset\; T\_\; M$ is a 2-plane containing $\backslash dot(t)$ and $\backslash widetilde\; \backslash subset\; T\_\; \backslash widetilde$ is a 2-plane containing $\backslash dot(t)|$ for all $t\; \backslash in\; (T)$. 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「Rauch comparison 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.