关于Gauss映射的一些结果(英文)

SOME RESULTS OF GAUSS MAPS

本文主要结果如下:1)将Lipschitz-Killing曲率沿单位法球丛的纤维积分可得Gauss曲率; 2)证明了曲面的关于广义Gauss映射象的面积,全中曲率的关系的一个公式;3)广义Gauss映射的球面象不可能在一个开半球内。

The main results of the paper are . 1) by integrating the Lipschitz-Killing curvature along the fibres of unit normal bundle one can get Gauss curvature; 2) prove an inequality befween the area of image of generalized Gauss map and the total mean curvature for surfaces ;3)prove that the spherical image of generalized Gauss map does not lie in any open hemisphere.