关于局部对称共形平坦黎曼流形上极小子流形的内蕴刚性  

The Minimal Submanifolds in a Locally Symmetric Conformally Flat Riemannian Manifold

作　　者：舒世昌 

机构地区：[1]咸阳师专数学系

出　　处：《工程数学学报》1996年第3期29-34,共6页Chinese Journal of Engineering Mathematics

基　　金：陕西省教委自然科学基金

摘　　要：设Ｍ是局部对称共形平坦黎曼流形Ｎｎ＋ｐ的紧致极小子流形，Ｋｃ和Ｑ分别是Ｍ上每点截面曲率和Ｒｉｃｃｉ曲率的下确界，Ｒ是Ｍ的数量曲率，本文利用三种内蕴量Ｋｃ，Ｑ和Ｒ所满足的适当关系。In this paper we prove the following theorems: Theorem 1 If M be a compact minimal submanifold of a Locally symmetric and conforally fiat riemannian manifold N n+p .If: (i) K c>-p-1pnR+1n+p-2 ×2(p-1)(n-1)+ppT c-t c-(p-1)(n-1)p(n+p-1)K , or (ii) K c>-12R+1n+p-2(n 2-n+1)T c-t c-n(n-1)2(n+p-1)K. then M is totally geodesic. Theorem 2 If: n≥4 (i) R>-2Q+1n+p-2(2n 2+2n-6)T c-2t c-n 2+n-4n+p-1K , or (ii) R<2npQ+nn+p-2 ×(2n-2)t c-p(4n-6)T c+2np-3p-n+1n+p-1K. then M is totally geodesic submanifold.

关 键 词：局部对称 共形平坦 子流形 黎曼流形 内蕴刚性 

分 类 号：O186.12[理学—数学]