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Displaying similar documents to “Isometry invariant Finsler metrics on Hilbert spaces”

On Finsler-Weyl manifolds and connections

Kozma, L.

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Let M be a manifold with all structures smooth which admits a metric g . Let Γ be a linear connection on M such that the associated covariant derivative satisfies g = g w for some 1-form w on M . Then one refers to the above setup as a Weyl structure on M and says that the pair ( g , w ) fits Γ . If σ : M and if ( g , w ) fits Γ , then ( e σ g , w + d σ ) fits Γ . Thus if one thinks of this as a map g w , then e σ g w + d σ .In this paper, the author attempts to apply Weyl’s idea above to Finsler spaces. A Finsler fundamental function L : T M satisfies...

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 ¯ 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 .

A framed f-structure on the tangent bundle of a Finsler manifold

Esmaeil Peyghan, Chunping Zhong (2012)

Annales Polonici Mathematici

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Let (M,F) be a Finsler manifold, that is, M is a smooth manifold endowed with a Finsler metric F. In this paper, we introduce on the slit tangent bundle T M ˜ a Riemannian metric G̃ which is naturally induced by F, and a family of framed f-structures which are parameterized by a real parameter c≠ 0. We prove that (i) the parameterized framed f-structure reduces to an almost contact structure on IM; (ii) the almost contact structure on IM is a Sasakian structure iff (M,F) is of constant flag...