3维双曲空间中给定平均曲率曲面的Weierstrass表示  

WEIERSTRASS REPRESENTATION FOR SURFACES OF PRESCRIBED MEAN CURVATURE IN THE HYPERBOLIC 3-DIMENSIONAL SPACE

作　　者：史淑国[1] 

机构地区：[1]复旦大学数学研究所,上海200433

出　　处：《数学年刊（A辑）》2001年第6期691-700,共10页Chinese Annals of Mathematics

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.

关 键 词：双曲空间 平均曲率 WEIERSTRASS表示 GAUSS映照 Betrami方程 可积条件 黎曼度量 

分 类 号：O186.12[理学—数学]