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arXiv · 0704.0317

Complete Shrinking Ricci Solitons have Finite Fundamental Group

William Wylie
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Abstract

We show that if a complete Riemannian manifold supports a vector field such that the Ricci tensor plus the Lie derivative of the metric with respect to the vector field has a positive lower bound, then the fundamental group is finite. In particular, it follows that complete shrinking Ricci solitons and complete smooth metric measure spaces with a positive lower bound on the Bakry-Emery tensor have finite fundamental group. The method of proof is to generalize arguments of Garcia-Rio and Fernandez-Lopez in the compact case.

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William Wylie. 2007-04-03. Complete Shrinking Ricci Solitons have Finite Fundamental Group. https://arxiv.org/abs/0704.0317

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