Complete gradient shrinking Ricci solitons have finite topological type
Differential Geometry
2008-01-03 v1 Geometric Topology
Abstract
We show that a complete Riemannian manifold has finite topological type (i.e., homeomorphic to the interior of a compact manifold with boundary), provided its Bakry-\'{E}mery Ricci tensor has a positive lower bound, and either of the following conditions: (i) the Ricci curvature is bounded from above; (ii) the Ricci curvature is bounded from below and injectivity radius is bounded away from zero. Moreover, a complete shrinking Ricci soliton has finite topological type if its scalar curvature is bounded.
Cite
@article{arxiv.0801.0103,
title = {Complete gradient shrinking Ricci solitons have finite topological type},
author = {Fuquan Fang and Jianwen man and Zhenlei Zhang},
journal= {arXiv preprint arXiv:0801.0103},
year = {2008}
}