Rotationally invariant constant mean curvature surfaces in homogeneous 3-manifolds

被引：29
|
作者：
Torralbo, Francisco [1 ]
机构：
[1] Univ Granada, Dept Geometria & Topol, E-18071 Granada, Spain
来源：
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2010年 / 28卷 / 05期
关键词：
Surfaces; Constant mean curvature; Homogeneous; 3-manifolds; Rotationally invariant surface; Berger spheres; SPACES;
D O I：
10.1016/j.difgeo.2010.04.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We classify constant mean curvature surfaces invariant by a 1-parameter group of isometries in the Berger spheres and in the special linear group SI(2, R). In particular, all constant mean curvature spheres in those spaces are described explicitly, proving that they are not always embedded. Besides new examples of Delaunay-type surfaces are obtained. Finally the relation between the area and volume of these spheres in the Berger spheres is studied, showing that, in some cases, they are not solution to the isoperimetric problem. (C) 2010 Elsevier B.V. All rights reserved.
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页码：593 / 607
页数：15
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