Some curvature pinching results for Riemannian manifolds with density

Abstract

In this note we consider versions of both Ricci and sectional curvature pinching for Riemannian manifold 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.

14 pages

References in corpus (2)

• Ricci flow with surgery on three-manifolds
• Positive weighted sectional curvature