n维双曲空间中给定Gauss映照的曲面的Weierstrass表示  

WEIERSTRASS REPRESENTATION FOR SURFACES OF PRESCRIBED GAUSS MAP IN THE HYPERBOLIC n-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）》2004年第3期345-350,共6页Chinese Annals of Mathematics

摘　　要：将双曲上半空间Hn中的曲面视为Rn中的曲面,导出这两种共形浸入下平均曲率向量的关系;证明了这两种浸入下Gauss映照是一样的;给出Hn中给定Gauss映照的曲面的Weierstrass表示;证明了一个唯一性结果.Considering the surfaces in hyperbolic space Hn as the ones in Rn, the author deduces the relation of mean curvature vectors about the two conformal immersions. The author proves that their Gauss map are same. The Weierstrass representation for surfaces of prescribed Gauss map in Hn and the result of uniqueness are obtained.

关 键 词：双曲空间 GAUSS映照 WEIERSTRASS表示 

分 类 号：O186.12[理学—数学]