A note on compact Weingarten hypersurfaces embedded in Rn+1

被引：0

作者：

de Lima, Eudes L. ^{[1
]}

机构：

[1] Univ Fed Campina Grande, Unidade Acad Ciencias Exatas & Nat, BR-58900000 Cajazeiras, Paraiba, Brazil

来源：

ARCHIV DER MATHEMATIK | 2018年 / 111卷 / 06期

关键词：

Weingarten hypersurface; Higher order mean curvature; Round sphere; CURVATURE;

D O I：

10.1007/s00013-018-1233-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the round sphere is the only compact Weingarten hypersurface embedded in the Euclidean space such that H-r = aH + b, for constants a, b is an element of R. Here, H-r stands for the r-th mean curvature and H denotes the standard mean curvature of the hypersurface.

引用

页码：669 / 672

页数：4

共 11 条

[1]

Alexandrov A.D., 1962, Ann. Mat. Pura Appl., V58, P303, DOI [10.1007/BF02413056, DOI 10.1007/BF02413056]

[2]

Alexandrov AD., 1958, Vestn. Leningr. Univ, V13, P14

[3]

[Anonymous], 1899, NACH KGL GES WISS MP

[4] SOME NEW CHARACTERIZATIONS OF THE EUCLIDEAN SPHERE [J].