翻訳と辞書 Words near each other ・ Schreder HP-12A ・ Schreder HP-13 ・ Schreder HP-14 ・ Schouteden's swift ・ Schoutedenapus ・ Schoutedenia lutea ・ Schoutedeniastes ・ Schoutedenius ・ Schoutedenius albogriseus ・ Schoutedenius gardneri ・ Schouten ・ Schouten Island ・ Schouten Islands ・ Schouten Islands (Papua New Guinea) ・ Schouten languages ・ Schouten tensor ・ Schoutenia ・ Schoutenia cornerii ・ Schoutenia furfuracea ・ Schoutenia kunstleri ・ Schouten–Nijenhuis bracket ・ Schouw ・ Schouwburg of Van Campen ・ Schouwburgplein ・ Schouwburgplein (Kortrijk) ・ Schouwburgplein (Rotterdam) ・ Schouweiler ・ Schouweiler railway station ・ Schouwen-Duiveland ・ Schowalter Foundation 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 Schouten tensor ： ウィキペディア英語版 Schouten tensor In Riemannian geometry, the Schouten tensor is a second-order tensor introduced by Jan Arnoldus Schouten. It is defined by, for ''n'' ≥ 3, :$P=\backslash frac\; \backslash left(Ric\; -\backslash frac\; g\backslash right)\backslash ,\; \backslash Leftrightarrow\; Ric=(n-2)\; P\; +\; J\; g\; \backslash ,\; ,$ where ''Ric'' is the Ricci tensor, ''R'' is the scalar curvature, ''g'' is the Riemannian metric, $J=\backslash fracR$ is the trace of ''P'' and ''n'' is the dimension of the manifold. The Weyl tensor equals the Riemann curvature tensor minus the Kulkarni–Nomizu product of the Schouten tensor with the metric. In an index notation :$R\_=W\_+g\_\; P\_-g\_\; P\_-g\_\; P\_+g\_\; P\_\backslash ,\; .$ The Schouten tensor often appears in conformal geometry because of its relatively simple conformal transformation law :$g\_\backslash mapsto\; \backslash Omega^2\; g\_\; \backslash Rightarrow\; P\_\backslash mapsto\; P\_-\backslash nabla\_i\; \backslash Upsilon\_j\; +\; \backslash Upsilon\_i\; \backslash Upsilon\_j\; -\backslash frac12\; \backslash Upsilon\_k\; \backslash Upsilon^k\; g\_\backslash ,\; ,$ where $\backslash Upsilon\_i\; :=\; \backslash Omega^\; \backslash partial\_i\; \backslash Omega\backslash ,\; .$ ==Further reading== *Arthur L. Besse, ''Einstein Manifolds''. Springer-Verlag, 2007. See Ch.1 §J "Conformal Changes of Riemannian Metrics." *Spyros Alexakis, ''The Decomposition of Global Conformal Invariants''. Princeton University Press, 2012. Ch.2, noting in a footnote that the Schouten tensor is a "trace-adjusted Ricci tensor" and may be considered as "essentially the Ricci tensor." *Wolfgang Kuhnel and Hans-Bert Rademacher, "Conformal diffeomorphisms preserving the Ricci tensor", ''Proc. Amer. Math. Soc.'' 123 (1995), no. 9, 2841–2848. Online (eprint ) (pdf). *T. Bailey, M.G. Eastwood and A.R. Gover, "Thomas's Structure Bundle for Conformal, Projective and Related Structures", Rocky Mountain Journal of Mathematics, vol. 24, Number 4, 1191-1217. 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「Schouten tensor」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.