On closed weingarten surfaces

被引：33

作者：

Kühnel, W ^{[1
]}

Steller, M ^{[1
]}

机构：

[1] Univ Stuttgart, Fachbereich Math, D-70550 Stuttgart, Germany

来源：

MONATSHEFTE FUR MATHEMATIK | 2005年 / 146卷 / 02期

关键词：

curvature diagram; surface of revolution; Hopf surface; Weingarten surface;

D O I：

10.1007/s00605-005-0313-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate closed surfaces in Euclidean 3-space satisfying certain functional relations kappa = F(lambda) between the principal curvatures kappa, lambda. In particular we find analytic closed surfaces of genus zero where F is a quadratic polynomial or F(lambda) = c lambda(2n+1). This generalizes results by H. Hopf on the case where F is linear and the case of ellipsoids of revolution where F(lambda) = c lambda(3).

引用

页码：113 / 126

页数：14

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