R^3中一类Blaschke张量迷向的旋转曲面

A class of rotation surfaces with isotropic Blaschke tensor in R^3

在Mbius几何中,Blaschke张量是一个很重要的Mbius不变量.对Blaschke张量迷向的超曲面进行分类是Mbius几何中的一个重要问题.在本文中,我们研究了R3中Blaschke张量迷向旋转曲面,得到了Blaschke张量迷向曲面的微分方程.最后,利用微分方程的解找到了一类Blaschke张量迷向旋转曲面。

Blaschke tensor is one of the most important MObius invariants in MObius geometry. One of the important questions in MObius geometry is to classify the hypersurfaces with isotropic Blaschke tensor. In this paper, we study rotation surface with isotropic Blaschke tensor in R3 , and derive the dif- ferential equation of the rotation surface with isotropic Blaschke tensor. Finally, we find a class of rota- tion surfaces with isotropic Blaschke tensor by making use of the solutions of the differential equation.