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arXiv · 1108.4628

Projective and Finsler metrizability: parameterization-rigidity of the geodesics

Ioan Bucataru·Zoltán Muzsnay
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Abstract

In this work we show that for the geodesic spray $S$ of a Finsler function $F$ the most natural projective deformation $\widetilde{S}=S -2 λF\mathbb C$ leads to a non-Finsler metrizable spray, for almost every value of $λ\in \mathbb R$. This result shows how rigid is the metrizablility property with respect to certain reparameterizations of the geodesics. As a consequence we obtain that the projective class of an arbitrary spray contains infinitely many sprays that are not Finsler metrizable.

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Ioan Bucataru, Zoltán Muzsnay. 2011-08-23. Projective and Finsler metrizability: parameterization-rigidity of the geodesics. https://doi.org/10.1142/s0129167x12500991

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