Some rigidity results for noncompact gradient steady Ricci solitons and Ricci-flat manifolds
Differential Geometry
2016-09-13 v2
Abstract
Gradient steady Ricci solitons are natural generalizations of Ricci-flat manifolds. In this article, we prove a curvature gap theorem for gradient steady Ricci solitons with nonconstant potential functions; and a curvature gap theorem for Ricci-flat manifolds, removing the volume growth assumptions in known results.
Keywords
Cite
@article{arxiv.1311.4515,
title = {Some rigidity results for noncompact gradient steady Ricci solitons and Ricci-flat manifolds},
author = {Fei He},
journal= {arXiv preprint arXiv:1311.4515},
year = {2016}
}
Comments
The result concerning ACyl manifolds was removed from the previous version since it can be generalized and does not depend on either Ricci soliton or Ricci-flat condition. 18 pages