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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 Projective vector field ： ウィキペディア英語版 Projective vector field A projective vector field (projective) is a smooth vector field on a semi Riemannian manifold (p.ex. spacetime) $M$ whose flow preserves the geodesic structure of $M$ without necessarily preserving the affine parameter of any geodesic. More intuitively, the flow of the projective maps geodesics smoothly into geodesics without preserving the affine parameter. ==Decomposition== In dealing with a vector field $X$ on a semi Riemannian manifold (p.ex. in general relativity), it is often useful to decompose the covariant derivative into its symmetric and skew-symmetric parts: :$X\_=\backslash frach\_+\; F\_$ where :$h\_=(\backslash mathcal\_X\; g)\_=X\_+X\_$ and :$F\_=\backslash frac(X\_-X\_)$ Note that $X\_a$ are the covariant components of $X$. 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「Projective vector field」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.