Abstract
In [17] A. Rapcsák obtained necessary and sufficient conditions for the projective Finsler metrizability in terms of a second order partial differential equations. In this paper we investigate the integrability of the Rapcsák system, consisting of the Rapcsák equations and the homogeneity condition, by using the Spencer version of the Cartan-Kähler theorem. We also consider the extended Rapcsák system, where the first integrability conditions are included.
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