Sectional curvature for Riemannian manifolds with density

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

In this paper we introduce two new notions of sectional curvature for Riemannian manifolds with density. Under both notions of curvature we classify the constant curvature manifolds. We also prove generalizations of the theorems of Cartan–Hadamard, Synge, and Bonnet–Myers as well as a generalization of the (non-smooth) 1/4-pinched sphere theorem. The main idea is to modify the radial curvature equation and second variation formula and then apply the techniques of classical Riemannian geometry to these new equations.

Original languageEnglish (US)
Pages (from-to)151-169
Number of pages19
JournalGeometriae Dedicata
Volume178
Issue number1
DOIs
StatePublished - Oct 24 2015

Keywords

  • Comparison geometry
  • Manifold with density
  • Sectional curvature

ASJC Scopus subject areas

  • Geometry and Topology

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