In this note we consider versions of both Ricci and sectional cur- vature 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.
|Original language||English (US)|
|Number of pages||14|
|Journal||Proceedings of the American Mathematical Society|
|State||Published - Feb 1 2016|
ASJC Scopus subject areas
- Applied Mathematics