Some framed $f$-structures on transversally Finsler foliations

Cristian Ida

Displaying similar documents to “Some framed $f$ -structures on transversally Finsler foliations”

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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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 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...

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.

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...

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...

Isometry invariant Finsler metrics on Hilbert spaces

Eugene Bilokopytov (2017)

Archivum Mathematicum

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In this paper we study isometry-invariant Finsler metrics on inner product spaces over $ℝ$ or $ℂ$ , i.e. the Finsler metrics which do not change under the action of all isometries of the inner product space. We give a new proof of the analytic description of all such metrics. In this article the most general concept of the Finsler metric is considered without any additional assumptions that are usually built into its definition. However, we present refined versions of the described results...

Natural liftings of foliations to the $r$ -tangent bunde

Mikulski, Włodzimierz M.

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Let $F$ be a $p$ -dimensional foliation on an $n$ -manifold $M$ , and $T^{r} M$ the $r$ -tangent bundle of $M$ . The purpose of this paper is to present some reltionship between the foliation $F$ and a natural lifting of $F$ to the bundle $T^{r} M$ . Let $L_{q}^{r} (F)$ $(q = 0, 1, \dots, r)$ be a foliation on $T^{r} M$ projectable onto $F$ and $L_{q}^{r} = {L_{q}^{r} (F)}$ a natural lifting of foliations to $T^{r} M$ . The author proves the following theorem: Any natural lifting of foliations to the $r$ -tangent bundle is equal to one of the liftings $L_{0}^{r}, L_{1}^{r}, \dots, L_{n}^{r}$ . The exposition is clear and well organized. ...

Warped compact foliations

Szymon M. Walczak (2008)

Annales Polonici Mathematici

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The notion of the Hausdorffized leaf space $\tilde{}$ of a foliation is introduced. A sufficient condition for warped compact foliations to converge to $\tilde{}$ is given. Moreover, a necessary condition for warped compact Hausdorff foliations to converge to $\tilde{}$ is shown. Finally, some examples are examined.

Lifts of Foliated Linear Connectionsto the Second Order Transverse Bundles

Vadim V. Shurygin, Svetlana K. Zubkova (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The second order transverse bundle $T_{}^{2} M$ of a foliated manifold $M$ carries a natural structure of a smooth manifold over the algebra $𝔻^{2}$ of truncated polynomials of degree two in one variable. Prolongations of foliated mappings to second order transverse bundles are a partial case of more general $𝔻^{2}$ -smooth foliated mappings between second order transverse bundles. We establish necessary and sufficient conditions under which a $𝔻^{2}$ -smooth foliated diffeomorphism between two second order transverse...

Displaying similar documents to “Some framed f -structures on transversally Finsler foliations”

Displaying similar documents to “Some framed $f$ -structures on transversally Finsler foliations”