On Finsler-Weyl manifolds and connections

Kozma, L.

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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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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...

Some framed $f$ -structures on transversally Finsler foliations

Cristian Ida (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Some problems concerning to Liouville distribution and framed $f$ -structures are studied on the normal bundle of the lifted Finsler foliation to its normal bundle. It is shown that the Liouville distribution of transversally Finsler foliations is an integrable one and some natural framed $f (3, ε)$ -structures of corank 2 exist on the normal bundle of the lifted Finsler foliation.

The $p$ -Laplace eigenvalue problem as $p \to \infty$ in a Finsler metric

M. Belloni, Bernhard Kawohl, P. Juutinen (2006)

Journal of the European Mathematical Society

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We consider the $p$ -Laplacian operator on a domain equipped with a Finsler metric. We recall relevant properties of its first eigenfunction for finite $p$ and investigate the limit problem as $p \to \infty$ .

On the conformal theory of Ichijyō manifolds

Szakál, Sz.

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Some special linear connection introduced in the Finsler space by Ichijyō has the property that the curvature tensors under conformal changes remain invariant. Two Ichijyō manifolds $(M, E, \nabla)$ and $(M, \bar{E}, \bar{\nabla})$ are said to be conformally equivalent if $\bar{E} = (exp σ^{v}) E$ , $σ \in C^{\infty} (M)$ .It is proved, that in this case, the following assertions are equivalent: 1. $σ$ is constant, 2. $h_{\nabla} = h_{\bar{\nabla}}$ , 3. $S_{\nabla} = S_{\bar{\nabla}}$ , 4. $t_{\nabla} = t_{\bar{\nabla}}$ .It is also proved (when the above conditions are satisfied) that1. If $(M, E, \nabla)$ is a generalized Berwald manifold, then $(M, \bar{E}, \bar{\nabla})$ is also a generalized Berwald...

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 $\bar{L} = e^{ϕ (x)} L$ .

Extension of smooth functions in infinite dimensions II: manifolds

C. J. Atkin (2002)

Studia Mathematica

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Let M be a separable $C^{\infty}$ Finsler manifold of infinite dimension. Then it is proved, amongst other results, that under suitable conditions of local extensibility the germ of a $C^{\infty}$ function, or of a $C^{\infty}$ section of a vector bundle, on the union of a closed submanifold and a closed locally compact set in M, extends to a $C^{\infty}$ function on the whole of M.

The Morse-Sard-Brown Theorem for Functionals on Bounded Fréchet-Finsler Manifolds

Kaveh Eftekharinasab (2015)

Communications in Mathematics

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In this paper we study Lipschitz-Fredholm vector fields on bounded Fréchet-Finsler manifolds. In this context we generalize the Morse-Sard-Brown theorem, asserting that if $M$ is a connected smooth bounded Fréchet-Finsler manifold endowed with a connection $𝒦$ and if $ξ$ is a smooth Lipschitz-Fredholm vector field on $M$ with respect to $𝒦$ which satisfies condition (WCV), then, for any smooth functional $l$ on $M$ which is associated to $ξ$ , the set of the critical values of $l$ is of first category...