On the Blaschke Isoparametric Hypersurfaces in the Unit Sphere

作     者：Xing Xiao LI Feng Yun ZHANG 

作者机构：Department of Mathematics. He'nan Normal University Xinxiang 453007 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2009年第25卷第4期

页      面：657-678页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：国家自然科学基金 

主　　题：Mobius form Blaschke eigenvalues Blaschke tensor Mobius metric Mobius second fundamental form 

摘      要：Given an immersed submanifold x ： M^M → S^n in the unit sphere S^n without umbilics, a Blaschke eigenvalue of x is by definition an eigenvalue of the Blaschke tensor of x. x is called Blaschke isoparametric if its Mobius form vanishes identically and all of its Blaschke eigenvalues are constant. Then the classification of Blaschke isoparametric hypersurfaces is natural and interesting in the MSbius geometry of submanifolds. When n = 4, the corresponding classification theorem was given by the authors. In this paper, we are able to complete the corresponding classification for n = 5. In particular, we shall prove that all the Blaschke isoparametric hypersurfaces in S^5 with more than two distinct Blaschke eigenvalues are necessarily Mobius isoparametric.