On the symplectic structure of the space of geodesics of a Hadamard manifold
type: Item
instance of: scholarly article
title: On the symplectic structure of the space of geodesics of a Hadamard manifold
zbMATH Open document ID: 0891.53028
DOI: 10.1023/A:1004945807350
author: Emmanuel Ferrand
published in: Geometriae Dedicata
publication date: 1998-07-06T00:00:00Z
review text: A Hadamard manifold is a simply connected manifold endowed with a complete Riemannian metric with negative or null sectional curvature. The author proves that the space of geodesics of a Hadamard manifold of dimension \(n\) is symplectomorphic to the cotangent bundle of the sphere of dimension \(n-1\). A generalization to Finsler metrics and an application to wave fronts are pointed out.
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 53B40
Mathematics Subject Classification ID: 58D15
zbMATH DE Number: 1098492
zbMATH Keywords: Hadamard manifolds
zbMATH Keywords: space of geodesics
zbMATH Keywords: symplectic structure
zbMATH Keywords: cotangent bundle
zbMATH Keywords: Finsler metric
zbMATH Keywords: wave front
reviewed by: Mircea Crasmareanu
MaRDI profile type: Publication
full work available at URL: a:1004945807350
OpenAlex ID: W173350268
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description: scientific article; zbMATH DE number 1098492