Trajectory equivalence and corresponding integrals
type: Item
instance of: scholarly article
title: Trajectory equivalence and corresponding integrals
zbMATH Open document ID: 0928.37003
published in: Regular and Chaotic Dynamics
publication date: 1999-05-05T00:00:00Z
review text: The authors show that if on a smooth manifold two Riemannian metrics exist which are geodesically equivalent then the related geodesic flow of any of these metrics is Liouville integrable. They also construct a nontrivial one-parameter family of geodesically equivalent metrics if there are two such metrics. Finally, they present a nontrivial metric on the \(n\)-dimensional ellipsoid geodesically equivalent to the standard one.
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 37K05
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 1281656
zbMATH Keywords: integrability
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: geodesic equivalence
zbMATH Keywords: Riemannian metrics
zbMATH Keywords: geodesic flow
zbMATH Keywords: Liouville integrable
author: Vladimir S. Matveev
author: Peter Topalov
reviewed by: L. M. Lerman
MaRDI profile type: Publication
DOI: 10.1070/RD1998V003N02ABEH000069
description: scientific article; zbMATH DE number 1281656