ON THE TOPOLOGY,VOLUME,DIAMETER AND GAUSS MAP IMAGE OF SUBMANIFOLDS IN A SPHERE  

作　　者：WUBINGYE 

机构地区：[1]DepartmentofMathematics,ZhejiangNormalUniversity,Jinhua321004,Zhejiang,China.

出　　处：《Chinese Annals of Mathematics,Series B》2004年第2期207-212,共6页数学年刊（B辑英文版）

基　　金：Project supported by the Fund of the Education Department of Zhejiang Province of China (No.20030707).

摘　　要：In this paper, the author uses Gauss map to study the topology, volume and diameter of submanifolds in a sphere. It is proved that if there exist ε, 1≥ε > 0 and a fixed unit simple p-vector a such that the Gauss map g of an n-dimensional complete and connected submanifold M in Sn+p satisfies (g, a) ≥ε, then M is diffeomorphic to Sn, and the volume and diameter of M satisfy εnvol(Sn) ≤vol(M) ≤ vol(Sn)/ε and επ ≤diam(M) ≤ π/ε, respectively. The author also characterizes the case where these inequalities become equalities. As an application, a differential sphere theorem for compact submanifolds in a sphere is obtained.

关 键 词：Gauss map VOLUME DIAMETER Differential sphere theorem 

分 类 号：O189.31[理学—数学]