A visual introduction to Riemannian curvatures and some discrete generalizations

Yann Ollivier 1, 2
2 TAO - Machine Learning and Optimisation
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
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.
Type de document :
Chapitre d'ouvrage
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
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https://hal.archives-ouvertes.fr/hal-00858008
Contributeur : Yann Ollivier <>
Soumis le : mercredi 4 septembre 2013 - 13:53:42
Dernière modification le : jeudi 5 avril 2018 - 12:30:12

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  • HAL Id : hal-00858008, version 1

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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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