On Submanifolds of the Unit Sphere with Vanishing Mobius Form and Parallel Para-Blaschke Tensor  

作　　者：Hong Ru SONG Xi Min LIU 

机构地区：[1]School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第2期347-370,共24页数学学报（英文版）

基　　金：Supported by Foundation of Natural Sciences of China(Grant Nos.11671121,11871197,11431009)。

摘　　要：The para-Blaschke tensor are extended in this paper from hypersurfaces to general higher codimensional submanifolds in the unit sphere S^(n),which is invariant under the Mobius transformations on Sn.Then some typical new examples of umbilic-free submanifolds in Snwith vanishing Mobius form and a parallel para-Blaschke tensor of two distinct eigenvalues,D_(1) and D_(2),are constructed.The main theorem of this paper is a simple characterization of these newly found examples in terms of the eigenvalues D_(1) and D_(2).

关 键 词：Parallel Blaschke tensor vanishing Mobius form constant scalar curvature parallel mean curvature vector field 

分 类 号：O186[理学—数学]