Three-dimensional manifolds having metrics with the same geodesics.
type: Item
instance of: scholarly article
title: Three-dimensional manifolds having metrics with the same geodesics.
zbMATH Open document ID: 1035.53117
DOI: 10.1016/S0040-9383(03)00004-1
author: Vladimir S. Matveev
published in: Topology
publication date: 2003-07-29T00:00:00Z
review text: The author proves that if two Riemannian metrics have the same geodesics on a closed three-dimensional manifold which is homeomorphic neither to a lens space nor to a Seifert manifold with zero Euler number, then the metrics are proportional.
Mathematics Subject Classification ID: 53D25
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 53C24
zbMATH DE Number: 1956008
zbMATH Keywords: Geodesic equivalence
zbMATH Keywords: Projectively equivalent metrics
zbMATH Keywords: Projective connection
zbMATH Keywords: Integrable system
zbMATH Keywords: Separation of variables
zbMATH Keywords: Geodesic rigidity
zbMATH Keywords: Liouville metric
zbMATH Keywords: Stäckel system
zbMATH Keywords: Obstructions to integrability
zbMATH Keywords: Local product structure
zbMATH Keywords: Lens space
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1956008