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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 Geodesic manifold ： ウィキペディア英語版 Geodesic manifold In mathematics, a complete manifold (or geodesically complete manifold) is a (pseudo-) Riemannian manifold for which every maximal (inextendible) geodesic is defined on $\backslash mathbb$. ==Examples== All compact Riemannian manifolds and all homogeneous manifolds are geodesically complete. Euclidean space $\backslash mathbb^$, the spheres $\backslash mathbb^$ and the tori $\backslash mathbb^$ (with their natural Riemannian metrics) are all complete manifolds. A simple example of a non-complete manifold is given by the punctured plane $M\; :=\; \backslash mathbb^\; \backslash setminus\; \backslash$ (with its induced metric). Geodesics going to the origin cannot be defined on the entire real line. There exists non geodesically complete compact pseudo-Riemannian (but not Riemannian) manifolds. It is the case for example of the Clifton–Pohl torus. 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「Geodesic 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.