Journal
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
Volume 31, Issue 3, Pages 405-415Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.difgeo.2013.02.001
Keywords
Isotropic sprays; Finsler metrizability; Flag curvature
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Funding
- Romanian National Authority for Scientific Research, CNCS UEFISCDI [PN-II-RU-TE-2011-3-0017]
- Hungarian Scientific Research Fund (OTKA) [K67617]
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In this paper we characterize sprays that are metrizable by Finsler functions of constant flag curvature. By solving a particular case of the Finsler metrizability problem, we provide the necessary and sufficient conditions that can be used to decide whether or not a given homogeneous system of second order ordinary differential equations represents the geodesic equations of a Finsler function of constant flag curvature. The conditions we provide are tensorial equations on the Jacobi endomorphism. We identify the class of homogeneous SODE where the Finsler metrizability is equivalent with the metrizability by a Finsler function of constant flag curvature. (C) 2013 Elsevier B.V. All rights reserved.
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