球面中极小子流形的整体刚性定理  

Global Rigidity Theorem for Minimal Submanifolds in Sphere

作　　者：蔡开仁[1] 

机构地区：[1]杭州师范学院数学系,杭州310036

出　　处：《工程数学学报》2003年第2期125-128,136,共5页Chinese Journal of Engineering Mathematics

摘　　要：建立了如下球面中极小子流形的整体刚性定理:假设M是标准球面中的一个n维紧致嵌入子流形,并设M具有平行平均曲率向量且Ricci曲率有正的下界(n-1)k。用σ表示M的第二基本形式长度的平方,于是必存在一个仅依赖n,k和平均曲率H的常数A,使得当σ的Ln 2模小于A时,M为球面的极小子流形。Let M be a compact submanifold with constant mean curvature vector and positive Ricci curvature embedded in the unit sphere Sn+p(1). By using a tensor , related to the second fundamental form, we set up a rigidity theorem. Denote by H,(n-1)k and ‖σ‖p the mean curvature, the positive lower bound of Ricci curvature and the Lp norm of the square langth of the second fundamental form of M respectively. It is shown that there is a constant A depending only on n,H and k such that if ‖σ‖n/2<A, then M is a minimal submanifold in sphere Sn+p-1(1+H2). 

关 键 词：Sobolev常数 平均曲率 子流形 

分 类 号：O186[理学—数学]