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Book Sections Year : 2013

A visual introduction to Riemannian curvatures and some discrete generalizations

Abstract

We try to provide a visual introduction to some objects used in Riemannian geometry: parallel transport, sectional curvature, Ricci curvature, Bianchi identities... We then explain some of the strategies used to define ana- logues of curvature in non-smooth or discrete spaces, beginning with Alexan- drov curvature and δ-hyperbolic spaces, and insisting on various notions of generalized Ricci curvature, which we briefly compare.
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Dates and versions

hal-00858008 , version 1 (04-09-2013)

Identifiers

  • HAL Id : hal-00858008 , version 1

Cite

Yann Ollivier. A visual introduction to Riemannian curvatures and some discrete generalizations. Galia Dafni, Robert McCann, Alina Stancu. Analysis and Geometry of Metric Measure Spaces: Lecture Notes of the 50th Séminaire de Mathématiques Supérieures (SMS), Montréal, 2011, AMS, pp. 197-219, 2013. ⟨hal-00858008⟩
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