Jet manifold associated to a Weil bundle

Ricardo J. Alonso

Displaying similar documents to “Jet manifold associated to a Weil bundle”

Natural affinors on the (r,s,q)-cotangent bundle of a fibered manifold

J. Kurek, W. M. Mikulski (2004)

Annales Polonici Mathematici

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For natural numbers r,s,q,m,n with s ≥ r ≤ q we describe all natural affinors on the (r,s,q)-cotangent bundle $T^{r, s, q *} Y$ over an (m,n)-dimensional fibered manifold Y.

Contact elements on fibered manifolds

Ivan Kolář, Włodzimierz M. Mikulski (2003)

Czechoslovak Mathematical Journal

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For every product preserving bundle functor $T^{μ}$ on fibered manifolds, we describe the underlying functor of any order $(r, s, q), s \geq r \leq q$ . We define the bundle $K_{k, l}^{r, s, q} Y$ of $(k, l)$ -dimensional contact elements of the order $(r, s, q)$ on a fibered manifold $Y$ and we characterize its elements geometrically. Then we study the bundle of general contact elements of type $μ$ . We also determine all natural transformations of $K_{k, l}^{r, s, q} Y$ into itself and of $T (K_{k, l}^{r, s, q} Y)$ into itself and we find all natural operators lifting projectable vector fields and horizontal...

Natural $T$ -functions on the cotangent bundle of a Weil bundle

Jiří M. Tomáš (2004)

Czechoslovak Mathematical Journal

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A natural $T$ -function on a natural bundle $F$ is a natural operator transforming vector fields on a manifold $M$ into functions on $F M$ . For any Weil algebra $A$ satisfying $dim M \geq w i d t h (A) + 1$ we determine all natural $T$ -functions on $T^{*} T^{A} M$ , the cotangent bundle to a Weil bundle $T^{A} M$ .

On the space of maps inducing isomorphic connections

T. R. Ramadas (1982)

Annales de l'institut Fourier

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Let $ω$ be the universal connection on the bundle $E U (n) \to B U (n)$ . Given a principal $U (n)$ -bundle $P \to M$ with connection $A$ , we determine the homotopy type of the space of maps $ϕ$ of $M$ into $B U (n)$ such that $(ϕ^{+} E U (n), ϕ^{+} ω)$ is isomorphic to $(P, A)$ . Here $ϕ^{+}$ denotes pull-back.

The contact system on the $(m, ℓ)$ -jet spaces

J. Muñoz, F. J. Muriel, Josemar Rodríguez (2001)

Archivum Mathematicum

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This paper is a continuation of [MMR:98], where we give a construction of the canonical Pfaff system $Ω (M_{m}^{ℓ})$ on the space of $(m, ℓ)$ -velocities of a smooth manifold $M$ . Here we show that the characteristic system of $Ω (M_{m}^{ℓ})$ agrees with the Lie algebra of $Aut (ℝ_{m}^{ℓ})$ , the structure group of the principal fibre bundle ${\overset{ˇ}{M}}_{m}^{ℓ} ⟶ J_{m}^{ℓ} (M)$ , hence it is projectable to an irreducible contact system on the space of $(m, ℓ)$ -jets ( $= ℓ$ -th order contact elements of dimension $m$ ) of $M$ . Furthermore, we translate to the language of Weil bundles the structure...

Displaying similar documents to “Jet manifold associated to a Weil bundle”

Natural affinors on the (r,s,q)-cotangent bundle of a fibered manifold

Contact elements on fibered manifolds

Natural T -functions on the cotangent bundle of a Weil bundle

On the space of maps inducing isomorphic connections

The contact system on the ( m , ℓ ) -jet spaces

Natural $T$ -functions on the cotangent bundle of a Weil bundle

The contact system on the $(m, ℓ)$ -jet spaces