Ricci solitons on locally conformally flat hypersurfaces in space forms

被引:12
|
作者
Cho, Jong Taek [1 ]
Kimura, Makoto [2 ]
机构
[1] Chonnam Natl Univ, Dept Math, Inst Basic Sci, Kwangju 500757, South Korea
[2] Shimane Univ, Fac Sci & Engn, Dept Math, Matsue, Shimane 6908504, Japan
基金
新加坡国家研究基金会;
关键词
Locally conformally flat hypersurfaces; Ricci solitons; Rotational hypersurfaces; GRADIENT SHRINKING SOLITONS; CLASSIFICATION;
D O I
10.1016/j.geomphys.2012.04.006
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study Ricci solitons on locally conformally flat hypersurfaces M-n in space forms (M) over tilde (n+1)(c) of constant sectional curvature c with potential vector field a principal curvature eigenvector of multiplicity one. We show that in Euclidean space, M-n is a hypersurface of revolution given in terms of a solution of some non-linear ODE. Hence there exists infinitely many mutually non-congruent Ricci solitons of this type. Furthermore when c >= 0 and M-n is complete, the Ricci soliton is gradient and in the case it is shrinking, M-n must be the product of the real line and the (n - 1)-sphere. (C) 2012 Elsevier B.V. All rights reserved.
引用
收藏
页码:1882 / 1891
页数:10
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