Some curvature pinching results for Riemannian manifolds with density

Wylie, William

doi:10.1090/proc/12853

Some curvature pinching results for Riemannian manifolds with density
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Proc. Amer. Math. Soc. 144 (2016), 823-836 Request permission

Abstract:

In this note we consider versions of both Ricci and sectional curvature pinching for Riemannian manifolds with density. In the Ricci curvature case the main result implies a diameter estimate that is new even for compact shrinking Ricci solitons. In the case of sectional curvature we prove a new sphere theorem.

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