Surfaces of Mk2 x R invariant under a one-parameter group of isometries

被引：0

作者：

Alencar, Hilario ^{[1
]}

do Carmo, Manfredo ^{[2
]}

Tribuzy, Renato ^{[3
]}

机构：

[1] Univ Fed Alagoas, Inst Matemat, BR-57072900 Maceio, AL, Brazil

[2] Inst Matematica Pura & Aplicada, BR-22460320 Rio De Janeiro, RJ, Brazil

[3] Univ Fed Amazonas, Dept Matemat, BR-63077000 Manaus, Amazonas, Brazil

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2014年 / 193卷 / 02期

关键词：

Product space; Hyperbolic plane; Isometry; One-parameter group; CURVATURE; SPACES;

D O I：

10.1007/s10231-012-0288-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We assume that an immersed constant mean curvature surface satisfies a relation involving the mean curvature, the Gaussian curvature and the angle that the unit vector of the factor makes with the normal to the surface. This relation, although given initially in its pointwise form, can be shown to be equivalent to an integral relation. From the assumed relation, it follows that is invariant under a one-parameter group of isometries of which are induced by the isometries of . An application is made to describe qualitatively those surfaces for which the Abresch-Rosenberg complex quadratic form vanishes.

引用

页码：517 / 527

页数：11

共 28 条

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