Displaying similar documents to “On affine transformations of Banachable bundles”

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...

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...

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.

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.

Natural differential operators between some natural bundles

Włodzimierz M. Mikulski (1993)

Mathematica Bohemica

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Let F and G be two natural bundles over n -manifolds. We prove that if F is of type (I) and G is of type (II), then any natural differential operator of F into G is of order 0. We give examples of natural bundles of type (I) or of type (II). As an application of the main theorem we determine all natural differential operators between some natural bundles.

The works of Charles Ehresmann on connections: from Cartan connections to connections on fibre bundles

Charles-Michel Marle (2007)

Banach Center Publications

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Around 1923, Élie Cartan introduced affine connections on manifolds and defined the main related concepts: torsion, curvature, holonomy groups. He discussed applications of these concepts in Classical and Relativistic Mechanics; in particular he explained how parallel transport with respect to a connection can be related to the principle of inertia in Galilean Mechanics and, more generally, can be used to model the motion of a particle in a gravitational field. In subsequent papers,...