单位球面上Mebius形式平行且仿Blaschke张量的特征值为常数的超曲面

对超曲面的分类是Mebius几何中感兴趣的课题。本文研究了单位球面上Mebius形式平行且仿Blaschke张量的特征值为常数的超曲面的分类问题。运用Blaschke张量的特征值,本文得到了一类超曲面的Mebius形式平行与Mebius形式为零之间的一些关系。在此基础上将钟定兴、孙弘安2008年得到的Mebius形式为零时单位球面上超曲面的分类定理推广到了Mebius形式平行的情形。

THE HYPERSURFACES WITH PARALLEL MOEBIUS FORM AND CONSTANT PARA-BLASCHKE EIGENVALUES IN UNIT SPHERES

It is interesting to classify hypersurfaces in Mebius geometry.We focus on the classification of hypersurfaces with parallel Mebius form and constant Para-Blaschke eigenvalues in unit spheres.Some relations between a class of hypersurfaces with parallel Mebius form and wanishing Mebius form are obtained based on Para-Blaschke eigenvalues.Furthermore,a theorem obtained by Zhong and Sun in 2008 on the classification of immersed hypersurfaces with wanishing Mebius form is generalized to the immersed hypersurfaces with parallel Mebius form in unit spheres.