Complete gradient shrinking Ricci solitons have finite topological type

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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-Émery 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.

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Differential Geometry, Geometric Topology

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http://salesiana.dossiersoluciones.com/handle/123456789/145103

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0801.0103
 http://arxiv.org/abs/0801.0103

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arXiv