English

Complete gradient shrinking Ricci solitons with pinched curvature

Differential Geometry 2014-10-10 v4

Abstract

We prove that any nn--dimensional complete gradient Ricci soliton with pinched Weyl curvature is a finite quotient of \RRn\RR^{n}, \RR×\SSn1\RR \times \SS^{n-1} or \SSn\SS^{n}. In particular, we do not need to assume the metric to be locally conformally flat.

Keywords

Cite

@article{arxiv.1104.0023,
  title  = {Complete gradient shrinking Ricci solitons with pinched curvature},
  author = {Giovanni Catino},
  journal= {arXiv preprint arXiv:1104.0023},
  year   = {2014}
}