摘要
首先叙述双曲空间中曲面的Ｇａｕｓｓ映照的定义；导出Ｇａｕｓｓ映照所满足的Ｂｅｌｔｒａｍｉ方程；给出了给定平均曲率曲面的Ｗｅｉｅｒｓｔｒａｓｓ表示公式；并讨论了这种表示的完全可积条件．
At the first, the author defines the Gauss map for surfaces in the hyperbolic space and prove that the Gauss map must satisfy a Beltrami equation. Next a representation formula for surfaces of prescribed mean curvature is obtained. The author also obtains a partial differential equations of two order for Gauss map and prove that this equation is the complete integrability condition of the above obtained representation.
出处
《数学年刊（A辑）》
CSCD
北大核心
2001年第6期691-700,共10页
Chinese Annals of Mathematics
