Some curvature pinching results for riemannian manifolds with density

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2 Scopus citations

Abstract

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 languageEnglish (US)
Pages (from-to)823-836
Number of pages14
JournalProceedings of the American Mathematical Society
Volume144
Issue number2
DOIs
StatePublished - Feb 1 2016

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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