On rotationally invariant shrinking gradient Ricci solitons

Brett Kotschwar

On rotationally invariant shrinking gradient Ricci solitons

微分几何 2007-05-23 v1 偏微分方程分析

作者: Brett Kotschwar

摘要

In this paper we study the gradient Ricci shrinking soliton equation on rotationally symmetric manifolds of dimension three and higher and prove that the only complete examples of such metrics on $S^n$ , $\R{n}$ and $\R{}\times S^{n-1}$ are, respectively, the round, flat, and standard cylindrical metrics.

关键词

ricci solitons ricci curvature and riemannian geometry riemannian geometry

引用

@article{arxiv.math/0702597,
  title  = {On rotationally invariant shrinking gradient Ricci solitons},
  author = {Brett Kotschwar},
  journal= {arXiv preprint arXiv:math/0702597},
  year   = {2007}
}

备注

14 pages

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