Displaying similar documents to “Lagrangians and Euler morphisms on fibered-fibered frame bundles from projectable-projectable classical linear connections”

The constructions of general connections on second jet prolongation

Mariusz Plaszczyk (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We determine all natural operators D transforming general connections Γ on fibred manifolds Y → M and torsion free classical linear connections ∇ on M into general connections D(Γ,∇) on the second order jet prolongation J2Y → M of Y → M.

Torsions of connections on higher order cotangent bundles

Miroslav Doupovec, Jan Kurek (2003)

Czechoslovak Mathematical Journal

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By a torsion of a general connection Γ on a fibered manifold Y → M we understand the Frölicher-Nijenhuis bracket of Γ and some canonical tangent valued one-form (affinor) on Y . Using all natural affinors on higher order cotangent bundles, we determine all torsions of general connections on such bundles. We present the geometrical interpretation and study some properties of the torsions.

On prolongation of higher order connections

Miroslav Doupovec, Włodzimierz M. Mikulski (2011)

Annales Polonici Mathematici

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We describe all bundle functors G admitting natural operators transforming rth order holonomic connections on a fibered manifold Y → M into rth order holonomic connections on GY → M. For second order holonomic connections we classify all such natural operators.

Connections on higher order principal prolongations

Vašík, Petr

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Geometric constructions of connections on the higher order principal prolongations of a principal bundle are considered. Moreover, the existing differences among connections on non-holonomic, semiholonomic and holonomic principal prolongations are discussed.

On third order semiholonomic prolongation of a connection

Petr Vašík (2011)

Banach Center Publications

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We recall several different definitions of semiholonomic jet prolongations of a fibered manifold and use them to derive some interesting properties of prolongation of a first order connection to a third order semiholonomic connection.

Torsions of connections on tangent bundles of higher order

Kureš, Miroslav

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The torsions of a general connection Γ on the r th-order tangent bundle of a manifold M are defined as the Frölicher-Nijenhuis bracket of Γ with the natural affinors. The author deduces the basic properties of these torsions. Then he compares them with the classical torsion of a principal connection on the r th-order frame bundle of M .