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On geodesic mappings of special Finsler spaces

Bácsó, Sándor — 1999

Proceedings of the 18th Winter School "Geometry and Physics"

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 ¯ n . The main result of this paper is as follows: if F n is of constant curvature K and the mapping F n ¯ n is a strongly geodesic mapping then K = 0 or K 0 and L ¯ = e ϕ ( x ) L .

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