Complete gradient shrinking Ricci solitons have finite topological type

Details Complete gradient shrinking Ricci solitons have finite topological type Complete gradient shrinking Ricci solitons have finite topological type

2007-12-31

arxiv.org/abs/0801.0103v1

Mathematics

Differential Geometry

Scientific paper

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.

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