A Myers-type theorem and compact Ricci solitons

Derdzinski, Andrzej

doi:10.1090/S0002-9939-06-08422-X

A Myers-type theorem and compact Ricci solitons
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Proc. Amer. Math. Soc. 134 (2006), 3645-3648 Request permission

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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