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...

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...

Groups of $C^{r, s}$ -diffeomorphisms related to a foliation

Jacek Lech, Tomasz Rybicki (2007)

Banach Center Publications

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The notion of a $C^{r, s}$ -diffeomorphism related to a foliation is introduced. A perfectness theorem for the group of $C^{r, s}$ -diffeomorphisms is proved. A remark on $C^{n + 1}$ -diffeomorphisms is given.

Correspondence between diffeomorphism groups and singular foliations

Tomasz Rybicki (2012)

Annales Polonici Mathematici

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It is well-known that any isotopically connected diffeomorphism group G of a manifold determines a unique singular foliation $ℱ_{G}$ . A one-to-one correspondence between the class of singular foliations and a subclass of diffeomorphism groups is established. As an illustration of this correspondence it is shown that the commutator subgroup [G,G] of an isotopically connected, factorizable and non-fixing $C^{r}$ diffeomorphism group G is simple iff the foliation $ℱ_{[G, G]}$ defined by [G,G] admits no proper...

Minimal, rigid foliations by curves on $ℂ ℙ^{n}$

Frank Loray, Julio C. Rebelo (2003)

Journal of the European Mathematical Society

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We prove the existence of minimal and rigid singular holomorphic foliations by curves on the projective space $ℂ ℙ^{n}$ for every dimension $n \geq 2$ and every degree $d \geq 2$ . Precisely, we construct a foliation $ℱ$ which is induced by a homogeneous vector field of degree $d$ , has a finite singular set and all the regular leaves are dense in the whole of $ℂ ℙ^{n}$ . Moreover, $ℱ$ satisfies many additional properties expected from chaotic dynamics and is rigid in the following sense: if $ℱ$ is conjugate to another holomorphic...

Bi-Legendrian connections

Beniamino Cappelletti Montano (2005)

Annales Polonici Mathematici

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We define the concept of a bi-Legendrian connection associated to a bi-Legendrian structure on an almost -manifold $M^{2 n + r}$ . Among other things, we compute the torsion of this connection and prove that the curvature vanishes along the leaves of the bi-Legendrian structure. Moreover, we prove that if the bi-Legendrian connection is flat, then the bi-Legendrian structure is locally equivalent to the standard structure on $ℝ^{2 n + r}$ .

Constructions on second order connections

J. Kurek, W. M. Mikulski (2007)

Annales Polonici Mathematici

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We classify all $ℱ ℳ_{m, n}$ -natural operators $: J ² ⟿ J ² V^{A}$ transforming second order connections Γ: Y → J²Y on a fibred manifold Y → M into second order connections $(Γ) : V^{A} Y \to J ² V^{A} Y$ on the vertical Weil bundle $V^{A} Y \to M$ corresponding to a Weil algebra A.

On prolongations of projectable connections

Jan Kurek, Włodzimierz M. Mikulski (2011)

Annales Polonici Mathematici

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We extend the concept of r-order connections on fibred manifolds to the one of (r,s,q)-order projectable connections on fibred-fibred manifolds, where r,s,q are arbitrary non-negative integers with s ≥ r ≤ q. Similarly to the fibred manifold case, given a bundle functor F of order r on (m₁,m₂,n₁,n₂)-dimensional fibred-fibred manifolds Y → M, we construct a general connection ℱ(Γ,Λ):FY → J¹FY on FY → M from a projectable general (i.e. (1,1,1)-order) connection $Γ : Y \to J^{1, 1, 1} Y$ on Y → M by means of an...

On canonical constructions on connections

Jan Kurek, Włodzimierz Mikulski (2016)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We study how a projectable general connection $Γ$ in a 2-fibred manifold $Y^{2} \to Y^{1} \to Y^{0}$ and a general vertical connection $Θ$ in $Y^{2} \to Y^{1} \to Y^{0}$ induce a general connection $A (Γ, Θ)$ in $Y^{2} \to Y^{1}$ .

Non-existence of some natural operators on connections

W. M. Mikulski (2003)

Annales Polonici Mathematici

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Let n,r,k be natural numbers such that n ≥ k+1. Non-existence of natural operators $C^{r} ₀ ⟿ Q (r e g T_{k}^{r} \to K_{k}^{r})$ and $C^{r} ₀ ⟿ Q (r e g T_{k}^{r *} \to K_{k}^{r *})$ over n-manifolds is proved. Some generalizations are obtained.

Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations

Andreas Höring (2014)

Annales de l’institut Fourier

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Let $X$ be a normal projective variety, and let $A$ be an ample Cartier divisor on $X$ . Suppose that $X$ is not the projective space. We prove that the twisted cotangent sheaf $Ω_{X} \otimes A$ is generically nef with respect to the polarisation $A$ . As an application we prove a Kobayashi-Ochiai theorem for foliations: if $ℱ ⊊ T_{X}$ is a foliation such that $det ℱ \equiv i_{ℱ} A$ , then $i_{ℱ}$ is at most the rank of $ℱ$ .

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

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