Displaying similar documents to “Affine structures on jet and Weil bundles”

Lagrangians and hamiltonians on affine bundles and higher order geometry

Paul Popescu, Marcela Popescu (2007)

Banach Center Publications

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The higher order bundles defined by an anchored bundle are constructed as a natural extension of the higher tangent spaces of a manifold. We prove that a hyperregular lagrangian (hyperregular affine hamiltonian) is a linearizable sub-lagrangian (affine sub-hamiltonian) on a suitable Legendre triple.

Affine liftings of torsion-free connections to Weil bundles

Jacek Dębecki (2009)

Colloquium Mathematicae

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This paper contains a classification of all affine liftings of torsion-free linear connections on n-dimensional manifolds to any linear connections on Weil bundles under the condition that n ≥ 3.

An affine framework for analytical mechanics

Paweł Urbański (2003)

Banach Center Publications

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An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and Hamiltonian formulations of the dynamics in the affine setting are proved.

On the natural transformations of Weil bundles

Ivan Kolář (2013)

Archivum Mathematicum

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First we deduce some general results on the covariant form of the natural transformations of Weil functors. Then we discuss several geometric properties of these transformations, special attention being paid to vector bundles and principal bundles.

New operators on jet spaces

L. Mangiarotti, Marco Modugno (1983)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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Product preserving gauge bundle functors on all principal bundle homomorphisms

Włodzimierz M. Mikulski (2011)

Annales Polonici Mathematici

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Let 𝓟𝓑 be the category of principal bundles and principal bundle homomorphisms. We describe completely the product preserving gauge bundle functors (ppgb-functors) on 𝓟𝓑 and their natural transformations in terms of the so-called admissible triples and their morphisms. Then we deduce that any ppgb-functor on 𝓟𝓑 admits a prolongation of principal connections to general ones. We also prove a "reduction" theorem for prolongations of principal connections into principal ones by means...