翻訳と辞書 Words near each other ・ Hypericum aphyllum ・ Hypericum ascyron ・ Hypericum asplundii ・ Hypercompe robusta ・ Hypercompe simplex ・ Hypercompe suffusa ・ Hypercompe tenebra ・ Hypercompe tessellata ・ Hypercompe testacea ・ Hypercompe theophila ・ Hypercompe trinitatis ・ Hypercompe turruptianoides ・ Hypercompetition ・ Hypercomplex analysis ・ Hypercomplex cell ・ Hypercomplex manifold ・ Hypercomplex number ・ Hypercomputation ・ Hyperconcentrated flow ・ Hypercone ・ Hypercone (spacecraft) ・ Hyperconjugation ・ Hyperconnected space ・ Hyperconnectivity ・ Hyperconsumerism ・ Hypercorrection ・ Hypercoryphodon ・ HyperCourseware ・ Hypercube ・ Hypercube graph 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 Hypercomplex manifold ： ウィキペディア英語版 Hypercomplex manifold In differential geometry, a hypercomplex manifold is a manifold with the tangent bundle equipped with an action by the algebra of quaternions in such a way that the quaternions $I,\; J,\; K$ define integrable almost complex structures. == Examples == Every hyperkähler manifold is also hypercomplex. The converse is not true. The Hopf surface :$\backslash bigg(\backslash backslash\; 0\backslash bigg)/$ (with $$ acting as a multiplication by a quaternion $q$, $|q|>1$) is hypercomplex, but not Kähler, hence not hyperkähler either. To see that the Hopf surface is not Kähler, notice that it is diffeomorphic to a product $S^1\backslash times\; S^3,$ hence its odd cohomology group is odd-dimensional. By Hodge decomposition, odd cohomology of a compact Kähler manifold are always even-dimensional. In fact H. Wakakuwa proved 〔 . 〕 that on a compact hyperkähler manifold $\backslash \; b\_\backslash equiv\; 0\; \backslash \; mod\; \backslash \; 4$. M. Verbitsky has shown that any compact hypercomplex manifold admitting a Kähler structure is also hyperkähler. In 1988, left-invariant hypercomplex structures on some compact Lie groups were constructed by the physicists Ph. Spindel, A. Sevrin, W. Troost, A. Van Proeyen. In 1992, D. Joyce rediscovered this construction, and gave a complete classification of left-invariant hypercomplex structures on compact Lie groups. Here is the complete list. :$$ T^4, SU(2l+1), T^1 \times SU(2l), T^l \times SO(2l+1), :$T^\backslash times\; SO(4l),\; T^l\; \backslash times\; Sp(l),\; T^2\; \backslash times\; E\_6,$ :$$ T^7\times E^7, T^8\times E^8, T^4\times F_4, T^2\times G_2 where $T^i$ denotes an $i$-dimensional compact torus. It is remarkable that any compact Lie group becomes hypercomplex after it is multiplied by a sufficiently big 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「Hypercomplex 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.