Hilbert forms for a Finsler metrizable projective class of sprays
type: Item
instance of: scholarly article
title: Hilbert forms for a Finsler metrizable projective class of sprays
zbMATH Open document ID: 1262.53064
author: Tom Mestdag
author: Mike Crampin
author: David J. Saunders
published in: Differential Geometry and its Applications
publication date: 2013-03-05T00:00:00Z
full work available at URL: https://arxiv.org/abs/1206.7021
review text: In terms of 2-forms on the slit tangent bundle, the authors establish necessary and sufficient conditions under which a projective-equivalence class of sprays is the geodesic class of a Finsler function, (so called metrizability conditions). Also, the relations between the known results [\textit{I. Bucataru} and \textit{Z. Muzsnay}, SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 114, 22 p. (2011; Zbl 1244.49072); \textit{J. C. Álvarez Paiva}, J. Differ. Geom. 69, No. 2, 353--378 (2005; Zbl 1088.53047)] are emphasized and it is shown that they are equivalent.
reviewed by: Nicoleta Aldea
Mathematics Subject Classification ID: 53C60
Mathematics Subject Classification ID: 53B40
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 6141622
zbMATH Keywords: spray
zbMATH Keywords: projective equivalence
zbMATH Keywords: geodesic path
zbMATH Keywords: path geometry
zbMATH Keywords: Finsler function
zbMATH Keywords: projective metrizability
zbMATH Keywords: Hilbert form
zbMATH Keywords: almost Grassmann structure
zbMATH Keywords: Jacobi field
zbMATH Keywords: totally-geodesic submanifold
MaRDI profile type: Publication
OpenAlex ID: W3105340774
Wikidata QID: Q115356648
arXiv ID: 1206.7021
DOI: 10.1016/J.DIFGEO.2012.10.012
description: scientific article