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A Myers-type theorem and compact Ricci solitons

Author: Andrzej Derdzinski
Journal: Proc. Amer. Math. Soc. 134 (2006), 3645-3648
MSC (2000): Primary 53C25; Secondary 53C20
Published electronically: June 13, 2006
MathSciNet review: 2240678
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Abstract: Let the Ricci curvature of a compact Riemannian manifold be greater, at every point, than the Lie derivative of the metric with respect to some fixed smooth vector field. It is shown that the fundamental group then has only finitely many conjugacy classes. This applies, in particular, to all compact shrinking Ricci solitons.

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Additional Information

Andrzej Derdzinski
Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210

Received by editor(s): December 8, 2004
Received by editor(s) in revised form: July 11, 2005
Published electronically: June 13, 2006
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.