Sprays metrizable by Finsler functions of constant flag curvature
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 seco...
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| Veröffentlicht in: | Differential geometry and its applications 2013-06, Vol.31 (3), p.405-415 |
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| creator | Bucataru, Ioan Muzsnay, Zoltán |
| description | 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. |
| doi_str_mv | 10.1016/j.difgeo.2013.02.001 |
| format | Article |
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| source | Elsevier ScienceDirect Journals; EZB-FREE-00999 freely available EZB journals |
| subjects | Curvature Differential equations Differential geometry Equivalence Finsler metrizability Flag curvature Flags Isotropic sprays Mathematical analysis Sprayers Sprays |
| title | Sprays metrizable by Finsler functions of constant flag curvature |
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