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- W3002014477 abstract "Abstract In this paper, we consider projective deformation of the geodesic system of Finsler spaces by holonomy invariant functions. Starting with a Finsler spray $S$ and a holonomy invariant function ${mathcal{P}}$ , we investigate the metrizability property of the projective deformation $widetilde{S}=S-2unicode[STIX]{x1D706}{mathcal{P}}{mathcal{C}}$ . We prove that for any holonomy invariant nontrivial function ${mathcal{P}}$ and for almost every value $unicode[STIX]{x1D706}in mathbb{R}$ , such deformation is not Finsler metrizable. We identify the cases where such deformation can lead to a metrizable spray. In these cases, the holonomy invariant function ${mathcal{P}}$ is necessarily one of the principal curvatures of the geodesic structure." @default.
- W3002014477 created "2020-01-30" @default.
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- W3002014477 date "2020-01-23" @default.
- W3002014477 modified "2023-09-25" @default.
- W3002014477 title "Metrizability of Holonomy Invariant Projective Deformation of Sprays" @default.
- W3002014477 doi "https://doi.org/10.4153/s0008439520000016" @default.
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