Complete Shrinking Ricci Solitons have Finite Fundamental Group

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dc.creatorWylie, William
dc.date2007-04-03
dc.date.accessioned2026-07-07T07:54:25Z
dc.date.available2026-07-07T07:54:25Z
dc.descriptionWe 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.
dc.description4 pages, To appear in Proceedings of AMS
dc.identifierhttps://arxiv.org/abs/0704.0317
dc.identifierhttp://arxiv.org/abs/0704.0317
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126602
dc.subjectDifferential Geometry
dc.subject53C20
dc.titleComplete Shrinking Ricci Solitons have Finite Fundamental Group
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