球空间 S^(n+p)(c)中的紧致极小子流形  

THE COMPACT MINIMAL SUBMANIFOLD IN SPHERE S^(n+p)(c)

作　　者：纪永强[1] 

机构地区：[1]宁夏大学

出　　处：《数学杂志》1990年第4期391-396,共6页Journal of Mathematics

摘　　要：设 M^n 是常曲率空间 S^(n+p)(c)的紧致极小子流形,设 K 和 Q 分别是 M^n 上每点各方向截面曲率和 Ricci 曲率的下确界,R 是 M^n 的数量曲率,本文利用 M^n 的内在量 KQ和 R,给出球空间中紧致极小子流形是全测地子流形的六个充分条件。Let M^n be an n—dimensional compact minimal submanifold in S^(n+p)(c)with constant curvature c(>0).Let K and Q be the infimum of the Sectionalcurvature and Ricci curvature of M^n respectively.Let R be the Scalarcurvature of M^n.In this paper,we obtain the following result:Let M^n be acompact minimal submanifold in S^(n+p)(c).if one of the following conditions issatisfied:(i)Q≥(n-1)c-n/2K,(ii)R>(n^2+2n-4)c-4Q,(iii)R>n(n-1)c-(np)/(p-1) c (p>1) (iv)K>1/2[n(n-1)c-R],(v)R>(n^2+n-4)c-2Q,(vi)R<n(n-1)c-np[(2n-3)c-2Q],then M^n is totally geodesic submanifold.

关 键 词：紧致 极小子流形 全测地子流形 

分 类 号：O186.16[理学—数学]