Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition

被引：0
|
作者：
Hyunjin Lee
Seonhui Kim
Young Jin Suh
机构：
[1] Kyungpook National University,Graduate School of Electrical Engineering University and Computer Science
[2] Kyungpook National University,Department of Mathematics
来源：
Czechoslovak Mathematical Journal | 2012年 / 62卷
关键词：
real hypersurface; complex two-plane Grassmannians; Hopf hypersurface; commuting shape operator; 53C50; 53C55;
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学科分类号：
摘要：
In this paper, first we introduce a new notion of commuting condition that φφ1A = Aφ1φ between the shape operator A and the structure tensors φ and φ1 for real hypersurfaces in G2(ℂm+2). Suprisingly, real hypersurfaces of type (A), that is, a tube over a totally geodesic G2(ℂm+1) in complex two plane Grassmannians G2(ℂm+2) satisfy this commuting condition. Next we consider a complete classification of Hopf hypersurfaces in G2(ℂm+2) satisfying the commuting condition. Finally we get a characterization of Type (A) in terms of such commuting condition φφ1A = Aφ1φ.
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页码：849 / 861
页数：12
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