黎曼流形的Killing张量场  

On the Killing Tensor Fields in a Compact Riemannian Manifold

作　　者：白正国[1] 

机构地区：[1]杭州大学数学系

出　　处：《杭州大学学报（自然科学版）》1990年第1期23-28,共6页Journal of Hangzhou University Natural Science Edition

基　　金：国家自然科学基金

摘　　要：关于紧的黎曼流形中的Killing张量场,已有若干研究,例如Mogi,Yano,Bochner,Hsiung,C.C.等.后者把前人一些结果推广到带边的紧的流形去,本文把熊的一些结果再加以改进.即不限于流形的边而对紧的黎曼流形中的某些超曲面进行研究.最后把所得结果应用到拟常曲率流形,得出相应的结论.We establish the following theorems: If a Killing vector field has zero tangential components on a hypersur-face Bn-1 of a compact Riemannian manifold Mn, then Bn-1 is a minimal hypersurface. If a Killing tensor field has zero tangential components on a totally umbilic hypersurface Bn-1 of Mn, then Bn-1 is totally geodesic. If a Killing tensor field with Kp≥0 has zero normal components on a Convex or concave or totally umbilic hypersurface Bn-1 of Mn, then Bn-1 is totally geodesic. The last theorem improves a theorem of C.C.Hsiung. Furthermore, we obtain some theorems for Killing fields in a compact Riemannian manifold of quasi constant curvature.

关 键 词：紧黎曼流形 Killing张量场 曲率 

分 类 号：O186.12[理学—数学]