On rotationally invariant shrinking gradient Ricci solitons

Brett Kotschwar

On rotationally invariant shrinking gradient Ricci solitons

Differential Geometry 2007-05-23 v1 Analysis of PDEs

Authors: Brett Kotschwar

Abstract

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.

Keywords

ricci solitons ricci curvature and riemannian geometry riemannian geometry

Cite

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

Comments

14 pages

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