On Mbius Form and Mbius Isoparametric Hypersurfaces  

作　　者：Ze Jun HU Xiao Li TIAN 

机构地区：[1]Department of Mathematics, Zhengzhou University, Zhengzhou 450052, P. R. China [2]Department of Humanities and Social Sciences, He 'nan Vocational and Technical College of Communications, Zhengzhou 450007, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2009年第12期2077-2092,共16页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant No.10671181)

摘　　要：An umbilic-free hypersurface in the unit sphere is called MSbius isoparametric if it satisfies two conditions, namely, it has vanishing MSbius form and has constant MSbius principal curvatures. In this paper, under the condition of having constant MSbius principal curvatures, we show that the hypersurface is of vanishing MSbius form if and only if its MSbius form is parallel with respect to the Levi-Civita connection of its MSbius metric. Moreover, typical examples are constructed to show that the condition of having constant MSbius principal curvatures and that of having vanishing MSbius form are independent of each other.An umbilic-free hypersurface in the unit sphere is called MSbius isoparametric if it satisfies two conditions, namely, it has vanishing MSbius form and has constant MSbius principal curvatures. In this paper, under the condition of having constant MSbius principal curvatures, we show that the hypersurface is of vanishing MSbius form if and only if its MSbius form is parallel with respect to the Levi-Civita connection of its MSbius metric. Moreover, typical examples are constructed to show that the condition of having constant MSbius principal curvatures and that of having vanishing MSbius form are independent of each other.

关 键 词：Mobius isoparametric hypersurface Mobius second fundamental form Mobius metric MSbius form paxallel Mobius form 

分 类 号：O186.11[理学—数学] TG659[理学—基础数学]