R^n中曲面的平均曲率向量

THE MEAN CURVATURE VECTOR OF SURFACES IN R^n

本文给出了R^n中曲面的平均曲率向量和Gauss映射之间所满足的偏微分方程,并把Kenmotsu给出的R^3中有指定平均曲率曲面的广义Weierstrass公式推广到n维欧氏空间。

In this paper we give the second order partial differential equation satisfied by the Gauss map of surfaces in R^n and generalize to a euclidean n-space the generalized Weierstrass formula with prescribed mean curvature.