3维双曲空间中曲面的双曲Gauss映照和法Gauss映照  

The Hyperbolic Gauss Map and Normal Gauss Map of Surfaces in 3-Dimensioual Hyperbolic Space

作　　者：史淑国[1] 

机构地区：[1]复旦大学数学研究所

出　　处：《数学学报（中文版）》2004年第1期1-10,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金973资助项目

摘　　要：本文导出了3维双曲空间中曲面的双曲Gauss映照和法Gauss映照的关系,发现了一般的曲面由双曲Gauss映照和平均曲率函数唯一确定,并证明了双曲Gauss映照所满足的二阶线性椭圆方程,给出了两种形式的关于双曲Gauss映照的三阶非线性偏微分方程(组)的一个解.In this paper, a relation between hyperbolic Gauss map and the normal Gauss map of surfaces in a 3-dimensional hyperbolic space has been obtained. It is proved that generic surfaces are determined uniquely by the hyperbolic Gauss map and the mean curvature function. A linear elliptic equation of second order for the hyperbolic Gauss map has been derived. The author also obtains a solution for two kinds of nonlinear partial differential equations (systems) of third order for the hyperbolic Gauss map.

关 键 词：双曲空间 双曲Gauss映照 法Gauss映照 

分 类 号：O186.12[理学—数学]