Ricci solitons on locally conformally flat hypersurfaces in space forms
Ricci solitons on locally conformally flat hypersurfaces in space forms
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DOI：
10.1016/j.geomphys.2012.04.006
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发表时间：
2012-08
影响因子：
1.5
通讯作者：
Jong Taek Cho;M. Kimura
中科院分区：
文献类型：
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作者：
Jong Taek Cho;M. Kimura
研究了局部共形平坦超曲面Mn在常截面曲率c空间形式M_n+1（c）中的Ricci孤子，其中势向量场是重数为1的主曲率特征向量.证明了在欧氏空间中，M是一个由非线性常微分方程的解给出的旋转超曲面。因此，存在无穷多个互不相合的这类Ricci孤子。此外，当c≥0且Mn是完备的时，Ricci孤子是梯度的，在它是收缩的情况下，Mn必须是真实的直线与（n−1）-球面的乘积。
We study Ricci solitons on locally conformally flat hypersurfaces Mnin space forms M˜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, Mnis 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 Mnis complete, the Ricci soliton is gradient and in the case it is shrinking, Mnmust be the product of the real line and the (n−1)-sphere.