拟常曲率空间的紧致极小子流形  

Minimal Submanifolds in a Riemannian Manifold of Quasi Constant Curvature

作　　者：舒世昌[1] 

机构地区：[1]陕西咸阳师范专科学校数学系

出　　处：《工程数学学报》1994年第3期48-54,共7页Chinese Journal of Engineering Mathematics

摘　　要：通过揭示拟常曲率空间中紧致极小子流形Ｍ的内在量Ｋ、Ｑ和Ｒ之间的关系，给出拟常曲率空间中紧致极小子流形是全测地子流形的几个充分条件，推广和包含了常曲率空间中Ｓ．Ｔ．Ｙａｕ的一个相应结果。Let M be an n-dimensional compact minimal submanifold in a Riemannian manifold Vn+p of quasi constant curvature,Let K and Q be the infinimum of the Sectional curvature and Ricci curvature of M respectively, Let R be the scalar cuvature of M.In this paper,we obtain some relations of K,Q and R,give some sufficient conditions for a compact minimal submanifold in Vn+p to be totally geodesic submanifold.In particular.When Vn+p is a manifold of constant curvature,i.e.b=0.We obtain the same result of S.T.Yau's Theorem.

关 键 词：拟常曲率空间 极小子流形 黎曼流形 

分 类 号：O186.12[理学—数学]