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On the projective Finsler metrizability and the integrability of Rapcsák equation

A. Rapcsák obtained necessary and sufficient conditions for the projective Finsler metrizability in terms of a second order partial differential system. In this paper we investigate the integrability of the Rapcsák system and the extended Rapcsák system, by using the Spencer version of the Cartan-Kähler theorem. We also consider the extended Rapcsák system completed with the curvature condition. W…