EINSTEIN-WEYL SPACE AND WEYL SUBMANIFOLD

爱因斯坦韦尔空间和韦尔子流形

基本信息

批准号：
10640098
负责人：
NARITA Fumio
金额：
$ 0.58万
依托单位：
AKITA NATIONAL COLLEGE OF TECHNOLOGY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

项目摘要

Let M be a manifold with a conformal structure [g] and a tortion-free affine connection D.I consider a Gauduchon manifold (M, g, D) with the Gauduchon metric g. Firstly, I obtained that a Gauduchon manifold (M, g, D) (n【greater than or equal】4) is a Gauduchon manifold of constant curvature if and only if (M, g, D) is a Weyl conformally flat Einstein-Weyl manifold. Next, I classified a Gauduchon manifold of constant curvature with Killing vector field. By using this result, I obtained the following result : Let (M, [g], D) be a compact Einstein-Weil manifold and Weyl conformally flat for every g【reverse surface chemistry arrow】[g]. If dimension n of M n【greater than or equal】4 and ω≠0 for every g【reverse surface chemistry arrow】[g], then (M, [g], D) is a Weyl flat manifold. Next, I investigated a Weyl submanifold of a Gauduchon manifold. Let (M, g, D) be a compact Weyl totally umbilical submanifold of a Gauduchon flat manifold which tangent to the Killing vector field B and ω≠0. Then M is a totally geodesic submanifold with Einstein-Weyl structure and the universal covering manifold of M is isometric to the Riemannian product of the sphere and R. If (M, g, D) is a Weyl hypersurface of a Gauduchon flat manifold which orthogonal to the Killing vector field B, then M is Weyl totally umbilical and a totally geodesic submanifold, moreover M is an elliptic space form. Finally, I obtained that (M, [g], J, D) admits an Einstein-Weyl structure if and only if (M, g, J) admits an Einstein-Hermitian structure.

令m为具有共形结构[g]和无动仿射连接的歧管。首先，我获得了gauduchon歧管（m，g，d）（n [大于或相等] 4）是恒定曲率的高uduchon歧管，并且仅当（m，g，d）是一个魏尔·韦尔（M，g，d）时，是一个韦伊尔的固结式爱因斯坦 - 韦尔·雷诺尔。接下来，我将恒定曲率的高图式分类与杀伤矢量场分类。通过使用此结果，我获得了以下结果：让（M，[G]，D）成为紧凑的Einstein-Weil歧管，而Weyl在每个g【反向表面化学箭头】[g]中均为平坦。如果每个g【反向表面化学箭头】[g]的m n【的尺寸n大于或等于】4和ω≠0，则（m，[g]，d）是Weyl Flat歧管。接下来，我研究了一个Weyl Submanifold LET（M，G，D）是一个紧凑的Weyl完全脐带，该圆锥形平面歧管是切线，该歧管与杀死载体场B和ω≠0相切。然后m是一个完全地球的亚曼叶夫，具有爱因斯坦 - 韦尔结构，M的普遍覆盖歧管与球体和R的riemannian产物相距。椭圆形空间形式。最后，我获得（M，[G]，J，D）在且仅当（M，G，J）允许Einstein-Hermitian结构时接受Einstein-Weyl结构。