Foliations in Information Geometry

21/09/2014
Publication MaxEnt 2014
OAI : oai:www.see.asso.fr:9603:11323
DOI :

Abstract

Foliations in Information Geometry

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application/pdf Foliations in Information Geometry Robert Wolak, Michel Nguiffo Boyom

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Foliations appear very naturally in the spaces considered in Information Geometry. In the paper we propose to present an introduction to the theory of those foliations which can be encountered in Information Geometry. We will develop the theory of foliation, both regular and singular, on Hessian manifolds as well as the theory of foliations transversely modelled on Hessian manifolds. Particular attention will be paid to foliation in small dimensions where the classification of those foliations is possible.