Commutative conservation laws for geodesic flows of metric admitting projective symmetry
type: Item
instance of: scholarly article
title: Commutative conservation laws for geodesic flows of metric admitting projective symmetry
zbMATH Open document ID: 1005.53065
published in: Mathematical Research Letters
publication date: 2003-02-25T00:00:00Z
review text: Suppose that a pseudo-Riemannian manifold \((M,g)\) admits a vector field \(X\) whose one-parameter group maps any geodesic line on some geodesic line (up to parametrization). Let \(r\) denote the maximal value on \(M\) of the degree of the minimal polynomial of \(((g^{ik} ({\mathcal L}_xg)_{kj}))_{ij}\). Then \(r\) explicit independent quadratic forms on \(TM\) are exhibited that are first integrals of the geodesic flow of \((M,g)\). This gives new first integrals of the geodesic flow, once a vector field preserving geodesic lines is known.
reviewed by: Jacques Franchi
Mathematics Subject Classification ID: 53D25
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 1751571
zbMATH Keywords: geodesic lines
zbMATH Keywords: geodesic flow
zbMATH Keywords: first integrals
zbMATH Keywords: pseudo-Riemannian manifold
author: Peter Topalov
MaRDI profile type: Publication
full work available at URL: mrl.2002.v9.n1.a5
OpenAlex ID: W1983334400
DOI: 10.4310/MRL.2002.V9.N1.A5
description: scientific article; zbMATH DE number 1751571