Isometry invariant Finsler metrics on Hilbert spaces

Eugene Bilokopytov

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

Decomposition of $H_{j k h}^{i} (x, \dot{x})$ in generalised recurrent Finsler space of second order

H. D. Pandey, V. J. Dubey (1982)

Matematički Vesnik

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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 $\nabla$ satisfies $\nabla g = g \otimes w$ 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 $σ : M \to ℝ$ and if $(g, w)$ fits $Γ$ , then $(e^{σ g}, w + d σ)$ fits $Γ$ . Thus if one thinks of this as a map $g \mapsto w$ , then $e^{σ g} \mapsto w + d σ$ .In this paper, the author attempts to apply Weyl’s idea above to Finsler spaces. A Finsler fundamental function $L : T M \to ℝ$ 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 ${\bar{F}}^{n} = (M^{n}, \bar{L})$ which map the geodesics of $F^{n}$ to geodesics of ${\bar{F}}^{n}$ (geodesic mappings).Now, he investigates the geodesic mappings between a Finsler space $F^{n}$ and a Riemannian space ${\bar{ℝ}}^{n}$ . The main result of this paper is as follows: if $F^{n}$ is of constant curvature $K$ and the mapping $F^{n} \to {\bar{ℝ}}^{n}$ is a strongly geodesic mapping then $K = 0$ or $K \neq 0$ and $\bar{L} = e^{ϕ (x)} L$ .

Beil metrics associated to a Finsler space.

Anastasiei, M., Shimada, H. (1998)

Balkan Journal of Geometry and its Applications (BJGA)

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Exempls of conics arising in two-dimensional Finsler and Lagrange geometries.

Constantinescu, Oana, Crasmareanu, Mircea (2009)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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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 $\tilde{T M}$ 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...

On a transformation of the Finsler metric

B. N. Prasad, H. S. Shukla, D. D. Singh (1990)

Matematički Vesnik

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Notes on new Finsler metric function.

Beil, R.G. (1997)

Balkan Journal of Geometry and its Applications (BJGA)

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