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The constructions of general connections on the fibred product of q copies of the first jet prolongation

100%

Plaszczyk M.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2018

tom 72

nr 1

We describe all natural operators \(A\) transforming general connections \(\Gamma\) on fibred manifolds \(Y \rightarrow M\) and torsion-free classical linear connections \(\Lambda\) on \(M\) into general connections \(A(\Gamma,\Lambda)\) on the fibred product \(J^{}Y \rightarrow M\) of \(q\) copies of the first jet prolongation \(J^{1}Y \rightarrow M\).

On naturality of some construction of connections

100%

Kurek J., Mikulski W.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2020

tom 74

nr 1

Let \(F\) be a bundle functor on the category of all fibred manifolds and fibred maps. Let \(\Gamma\) be a general connection in a fibred manifold \(\mathrm{pr}:Y\to M\) and \(\nabla\) be a classical linear connection on \(M\). We prove that the well-known general connection \(\mathcal{F}(\Gamma,\nabla)\) in \(FY\to M\) is canonical with respect to fibred maps and with respect to natural transformations of bundle functors.

Ograniczanie wyników

2 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

1 Kurek J.

1 Mikulski W.

1 Plaszczyk M.

1 2020

1 2018

Wyniki wyszukiwania

The constructions of general connections on the fibred product of q copies of the first jet prolongation

On naturality of some construction of connections