Sectional curvature for Riemannian manifolds with density

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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
Issue number1
StatePublished - Oct 24 2015


  • Comparison geometry
  • Manifold with density
  • Sectional curvature

ASJC Scopus subject areas

  • Geometry and Topology

Fingerprint Dive into the research topics of 'Sectional curvature for Riemannian manifolds with density'. Together they form a unique fingerprint.

Cite this