黎曼流形中紧子流形的拼挤定理(英文)  

Pinching Theorem for Compact Submanifold in Riemannian Manifold

作　　者：程立正[1] 

机构地区：[1]湖南涉外经济学院理学部,长沙410205

出　　处：《数学理论与应用》2008年第3期73-76,共4页Mathematical Theory and Applications

摘　　要：本利用几何不等式和曲率估计的方法,证明了黎曼流形Nn+p上的具有平行平均曲率的紧子流形Mn上的一个拼挤定理。若N上的截曲率KN满足-1≤KN≤δ≤0,且‖S-nH2‖n/2,‖S-nH2‖n/n-2满足一些不等式,则δ=-1。Making use of geometric inequalities and curvature estimates, I prove a pinching theorem of compact submanifolds M^n with parallel mean curvature in a complete simply conneted Riemannian manifold N^n＋p with nonpositive sectional curva- ture.If the sectional curvature of N KN satisfy - 1≤ KN≤δ≤0. and ‖S- nH2‖n/2, ‖ S-nH^2‖n/n-s satisfy some inequalities,then δ= - 1.

关 键 词：拼挤定理 子流形 非负截曲率 

分 类 号：O186.12[理学—数学] O184[理学—基础数学]