Geometry of contrast functions and conformal geometry
type: Item
instance of: scholarly article
title: Geometry of contrast functions and conformal geometry
zbMATH Open document ID: 0949.53017
author: Hiroshi Matsuzoe
published in: Hiroshima Mathematical Journal
publication date: 2000-11-23T00:00:00Z
review text: In information geometry, a statistical manifold is a pseudo-Riemannian manifold \((M,h)\) with distinguished torsion-free affine connection \(\nabla\) such that the covariant derivative \(\nabla h\) is symmetric. A contrast function on a smooth manifold \(M\) is a function on \(M\times M\) with specific properties. In particular, each contrast function defines two torsion free connections \(\nabla \) and \(\nabla^*\) and a pseudo-Riemannian metric \(h\) on \(M\). The resulting induced objects \((M,h, \nabla)\) and \((M,h,\nabla^*)\) are called dual statistical manifolds. The Barlett tensors of these structures turn out to be derived from the fourth order derivatives of the contrast function and they are used to express necessary and sufficient conditions for these structures to be projectively flat, dual-projectively flat or conformally flat.
reviewed by: Jan Slovák
Mathematics Subject Classification ID: 53B30
Mathematics Subject Classification ID: 62B10
Mathematics Subject Classification ID: 53A15
zbMATH DE Number: 1310265
zbMATH Keywords: contrast function
zbMATH Keywords: statistical manifold
zbMATH Keywords: curvature tensor
zbMATH Keywords: affine immersion
zbMATH Keywords: Barlett tensor
zbMATH Keywords: projectively flat
zbMATH Keywords: conformally flat
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1206125160
OpenAlex ID: W1512660147
DOI: 10.32917/HMJ/1206125160
description: scientific article; zbMATH DE number 1310265