Displaying similar documents to “Projective invariants of an orthogonal ennuple in a Finsler space”

On geodesic mappings of special Finsler spaces

Bácsó, Sándor

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The author previously studied with and [Publ. Math. 42, 139-144 (1993; Zbl 0796.53022)] the diffeomorphisms between two Finsler spaces F n = ( M n , L ) and F ¯ n = ( M n , L ¯ ) which map the geodesics of F n to geodesics of F ¯ n (geodesic mappings).Now, he investigates the geodesic mappings between a Finsler space F n and a Riemannian space ℝ ¯ n . The main result of this paper is as follows: if F n is of constant curvature K and the mapping F n → ℝ ¯ n is a strongly geodesic mapping then K = 0 or K ≠ 0 and L ¯ = e ϕ ( x ) L .

On the projective Finsler metrizability and the integrability of Rapcsák equation

Tamás Milkovszki, Zoltán Muzsnay (2017)

Czechoslovak Mathematical Journal

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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. We prove that in the non-isotropic case there is a nontrivial Spencer cohomology group in...