Averaged Riemannian metrics and connections with application to locally conformal Berwald manifolds
type: Item
instance of: scholarly article
title: Averaged Riemannian metrics and connections with application to locally conformal Berwald manifolds
zbMATH Open document ID: 1299.53049
DOI: 10.5486/PMD.2012.5226
author: Tadashi Aikou
published in: Publicationes Mathematicae Debrecen
publication date: 2012-09-17T00:00:00Z
Mathematics Subject Classification ID: 53B40
zbMATH DE Number: 6083260
zbMATH Keywords: Finsler metrics
zbMATH Keywords: averaged metrics
zbMATH Keywords: averaged connections
zbMATH Keywords: locally conformal Berwald spaces
Wikidata QID: Q115159428
MaRDI profile type: Publication
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review text: The author recalls in his own formalism the notion of averaged Riemannian metric and averaged connection defined in [\textit{R. Gallego Torrome} and \textit{F. Etayo}, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 104, No. 1, 69--80 (2010; Zbl 1197.53023)]. Then he proves, among other, the following:NEWLINENEWLINENEWLINEi) If \((M,L)\) is a Landsberg manifold and \(g\) is the averaged metric for \((M,L)\), then the covariant derivative \(\nabla\) obtained from the Berwald derivative \(D\) of \((M,L)\) is the Levi-Civita derivation of \(g\).NEWLINENEWLINENEWLINEii) If \((M,L)\) is a locally conformal Berwald manifold and \(g\) is the averaged Riemannian metric for \((M,L)\), and the free-torsion covariant derivative \(\nabla\) satisfies a certain condition then \(\nabla\) is the Weyl connection for the conformal class of \(g\).
reviewed by: Mihai Anastasiei
description: scientific article; zbMATH DE number 6083260