Ricci solitons on locally conformally flat hypersurfaces in space forms

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• 作者：Jong Taek Cho^a ; ^{jtcho@chonnam.ac.kr} ; Makoto Kimura^b ; ^{mkimura@riko.shimane-u.ac.jp} ; ^{kmakoto@sci.ibaraki.ac.jp}
• 关键词：Locally conformally flat hypersurfaces ; Ricci solitons ; Rotational hypersurfaces
• 刊名：Journal of Geometry and Physics
• 出版年：2012
• 期刊代码：29_03930440
• 类别：ph
• 出版时间：August, 2012
• 卷：62
• 期：8
• 页码：1882-1891
• 文件大小：239 K

摘要

We study Ricci solitons on locally conformally flat hypersurfaces in space forms of constant sectional curvature with potential vector field a principal curvature eigenvector of multiplicity one. We show that in Euclidean space, 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 and is complete, the Ricci soliton is gradient and in the case it is shrinking, must be the product of the real line and the -sphere.