On the Finsler-metrizabilities of spray manifolds
type: Item
instance of: scholarly article
title: On the Finsler-metrizabilities of spray manifolds
zbMATH Open document ID: 0997.53056
DOI: 10.1023/A:1014928103275
published in: Periodica Mathematica Hungarica
publication date: 2002-11-03T00:00:00Z
review text: Using the local coordinate apparatus, \textit{A. Rapcsák} [Publ. Math. (Debrecen) 8, 285-290 (1961; Zbl 0101.39901); Ann. Mat. Pura Appl. IV Ser. 57, (233-238 (1962; Zbl 0105.15901); Publ. Math. (Debrecen) 9, 164-167 (1962; Zbl 0129.36004)] gave necessary and sufficient conditions, expressed in second order PDEs for a Finsler space to be projectively related to a spray (path-space), and for the metrizability of a spray (path-space). In this selfcontained paper the authors first give a modern version and reformulation in terms of 0-homogeneous Hilbert 1-forms of Rapcsák's and other Finsler metrizability problems which include also the classical inverse problem of the calculus of variation, and then they reduce Rapcsák's equations to a first order PDE and an algebraic condition.
Mathematics Subject Classification ID: 53C60
zbMATH DE Number: 1822355
zbMATH Keywords: Finsler-metrizability
author: József Szilasi
author: Sz. Vattamány
reviewed by: Lajos Tamássy
MaRDI profile type: Publication
full work available at URL: a:1014928103275
OpenAlex ID: W1798625708
description: scientific article; zbMATH DE number 1822355