On Submanifolds of the Unit Sphere with Vanishing M(o)bius Form and Parallel Para-Blaschke Tensor

• 作者: Hong Ru SONG Xi Min LIU
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2022,（2）
• 页码范围: 347-370
• 页数: 24页
• 语种: 英文

摘要

The para-Blaschke tensor are extended in this paper from hypersurfaces to general higher codimensional submanifolds in the unit sphere Sn,which is invariant under the M(o)bius transformations on Sn.Then some typical new examples of umbilic-free submanifolds in Sn with vanishing M(o)bius form and a parallel para-Blaschke tensor of two distinct eigenvalues,D1 and D2,are constructed.The main theorem of this paper is a simple characterization of these newly found examples in terms of the eigenvalues D1 and D2.