Some curvature pinching results for Riemannian manifolds with density
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- by William Wylie
- Proc. Amer. Math. Soc. 144 (2016), 823-836
- DOI: https://doi.org/10.1090/proc/12853
- Published electronically: August 26, 2015
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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.References
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Bibliographic Information
- William Wylie
- Affiliation: Department of Mathematics, 215 Carnegie Building, Syracuse University, Syracuse, New York 13244
- MR Author ID: 792291
- Email: wwylie@syr.edu
- Received by editor(s): January 24, 2015
- Published electronically: August 26, 2015
- Communicated by: Lei Ni
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 823-836
- MSC (2010): Primary 53C25
- DOI: https://doi.org/10.1090/proc/12853
- MathSciNet review: 3430857