期刊
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
卷 31, 期 3, 页码 405-415出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.difgeo.2013.02.001
关键词
Isotropic sprays; Finsler metrizability; Flag curvature
资金
- Romanian National Authority for Scientific Research, CNCS UEFISCDI [PN-II-RU-TE-2011-3-0017]
- Hungarian Scientific Research Fund (OTKA) [K67617]
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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