Sectional curvature for Riemannian manifolds with density

Research output: Research - peer-reviewArticle

  • 3 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.

LanguageEnglish (US)
Pages151-169
Number of pages19
JournalGeometriae Dedicata
Volume178
Issue number1
DOIs
StatePublished - Oct 24 2015

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Sectional Curvature
Riemannian Manifold
Curvature
Generalization
Sphere Theorem
Second Variation
Riemannian geometry
Classify
Theorem

Keywords

  • Comparison geometry
  • Manifold with density
  • Sectional curvature

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Sectional curvature for Riemannian manifolds with density. / Wylie, William.

In: Geometriae Dedicata, Vol. 178, No. 1, 24.10.2015, p. 151-169.

Research output: Research - peer-reviewArticle

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