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Displaying similar documents to “Natural Transformations of Symmetric Affine Connections on Manifolds to Metrics on Linear Frame Bundles: a Classification.”

Affine structures on jet and Weil bundles

David Blázquez-Sanz (2009)

Colloquium Mathematicae

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Weil algebra morphisms induce natural transformations between Weil bundles. In some well known cases, a natural transformation is endowed with a canonical structure of affine bundle. We show that this structure arises only when the Weil algebra morphism is surjective and its kernel has null square. Moreover, in some cases, this structure of affine bundle passes to jet spaces. We give a characterization of this fact in algebraic terms. This algebraic condition also determines an affine...

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.

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.

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.