A Note on hypersurfaces of a Euclidean space

被引：3

作者：

Deshmukh, Sharief ^{[1
]}

机构：

[1] King Saud Univ, Dept Math, Coll Sci, Riyadh 11451, Saudi Arabia

来源：

COMPTES RENDUS MATHEMATIQUE | 2013年 / 351卷 / 15-16期

关键词：

D O I：

10.1016/j.crma.2013.09.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this short Note, we consider a compact and connected orientable hypersurface M of the Euclidean space Rn+1 with non-negative support function and Minkowski's integrand sigma, and show that the mean curvature function alpha is the solution of the Poisson equation Delta phi = sigma if and only if M is isometric to n-sphere S-n(c) of constant curvature c. A similar result is proved for a hypersurface with scalar curvature satisfying the Poisson equation Delta phi = sigma. (C) 2013 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

引用

页码：631 / 634

页数：4