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PROJECTIVE AND FINSLER METRIZABILITY: PARAMETERIZATION-RIGIDITY OF THE GEODESICS

    https://doi.org/10.1142/S0129167X12500991Cited by:12 (Source: Crossref)

    In this work we show that for the geodesic spray S of a Finsler function F, the most natural projective deformation leads to a non-Finsler metrizable spray, for almost every value of λ ∈ 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.

    AMSC: 53C60, 58B20, 49N45, 58E30

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