The Gauss map of submanifolds in the Heisenberg group

被引：0
|
作者：
Petrov, E. V. [1 ]
机构：
[1] Kharkov Natl Univ, UA-61022 Kharkov, Ukraine
来源：
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2011年 / 29卷 / 04期
关键词：
Heisenberg group; Gauss map; Harmonic map; Mean curvature field; Constant mean curvature hypersurface;
D O I：
10.1016/j.difgeo.2011.04.036
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We obtain criteria for the harmonicity of the Gauss map of submanifolds in the Heisenberg group and consider the examples demonstrating the connection between the harmonicity of this map and the properties of the mean curvature field. Also, we introduce a natural class of cylindrical submanifolds and prove that a constant mean curvature hypersurface with harmonic Gauss map is cylindrical. (C) 2011 Elsevier B.V. All rights reserved.
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页码：516 / 532
页数：17
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