翻訳と辞書 Words near each other ・ Hyperolius ・ Hyperolius acuticephalus ・ Hyperolius acuticeps ・ Hyperolius acutirostris ・ Hyperkalemia ・ Hyperkalemic periodic paralysis ・ Hyperkatifeia ・ Hyperkeratinization ・ Hyperkeratosis ・ Hyperkeratotic cutaneous capillary-venous malformation ・ Hyperkeratotic hand dermatitis ・ Hyperkind ・ Hyperkinesia ・ Hyperkinesis ・ Hyperkinetic disorder ・ Hyperkähler manifold ・ Hyperkähler quotient ・ Hyperlais ・ Hyperlais argillacealis ・ Hyperlais conspersalis ・ Hyperlais cruzae ・ Hyperlais dulcinalis ・ Hyperlais glyceralis ・ Hyperlais nemausalis ・ Hyperlais rivasalis ・ Hyperlais rosseti ・ Hyperlais siccalis ・ Hyperlais squamosa ・ Hyperlais transversalis ・ Hyperlais xanthomista 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 Hyperkähler manifold ： ウィキペディア英語版 Hyperkähler manifold In differential geometry, a hyperkähler manifold is a Riemannian manifold of dimension 4''k'' and holonomy group contained in Sp(''k'') (here Sp(''k'') denotes a compact form of a symplectic group, identified with the group of quaternionic-linear unitary endomorphisms of a $k$-dimensional quaternionic Hermitian space). Hyperkähler manifolds are special classes of Kähler manifolds. They can be thought of as quaternionic analogues of Kähler manifolds. All hyperkähler manifolds are Ricci-flat and are thus Calabi–Yau manifolds (this can be easily seen by noting that Sp(''k'') is a subgroup of SU(2''k'')). Hyperkähler manifolds were defined by E. Calabi in 1978. ==Quaternionic structure== Every hyperkähler manifold ''M'' has a 2-sphere of complex structures (i.e. integrable almost complex structures) with respect to which the metric is Kähler. In particular, it is an almost quaternionic manifold, meaning that there are three distinct complex structures, ''I'', ''J,'' and ''K,'' which satisfy the quaternion relations :$I^2\; =\; J^2\; =\; K^2\; =\; IJK\; =\; -1.\backslash ,$ Any linear combination :$aI\; +\; bJ\; +\; cK\; \backslash ,$ with $a,\; b,\; c$ real numbers such that :$a^2\; +\; b^2\; +\; c^2\; =\; 1\; \backslash ,$ is also a complex structure on ''M''. In particular, the tangent space ''T''''x''''M'' is a quaternionic vector space for each point ''x'' of ''M''. Sp(''k'') can be considered as the group of orthogonal transformations of $\backslash mathbb^=\backslash mathbb^k$ which are linear with respect to ''I'', ''J'' and ''K''. From this it follows that the holonomy of the manifold is contained in Sp(''k''). Conversely, if the holonomy group of the Riemannian manifold ''M'' is contained in Sp(''k''), choose complex structures ''I''''x'', ''Jx'' and ''K''''x'' on ''T''''x''''M'' which make ''T''''x''''M'' into a quaternionic vector space. Parallel transport of these complex structures gives the required quaternionic structure on ''M''. 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「Hyperkähler 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.