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Displaying similar documents to “From the Fermi-Walker to the Cartan connection”

A construction of a connection on G Y → Y from a connection on Y → M by means of classical linear connections on M and Y

Włodzimierz M. Mikulski (2005)

Commentationes Mathematicae Universitatis Carolinae

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Let G be a bundle functor of order ( r , s , q ) , s ≥ r ≤ q , on the category ℱ ℳ m , n of ( m , n ) -dimensional fibered manifolds and local fibered diffeomorphisms. Given a general connection Γ on an ℱ ℳ m , n -object Y → M we construct a general connection 𝒢 ( Γ , λ , Λ ) on G Y → Y be means of an auxiliary q -th order linear connection λ on M and an s -th order linear connection Λ on Y . Then we construct a general connection 𝒢 ( Γ , ∇ 1 , ∇ 2 ) on G Y → Y by means of auxiliary classical linear connections ∇ 1 on M and ∇ 2 on Y . In the case G = J 1 we determine all general connections...

Non-existence of some canonical constructions on connections

Włodzimierz M. Mikulski (2003)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

For a vector bundle functor H : ℳ f → 𝒱 ℬ with the point property we prove that H is product preserving if and only if for any m and n there is an ℱ ℳ m , n -natural operator D transforming connections Γ on ( m , n ) -dimensional fibered manifolds p : Y → M into connections D ( Γ ) on H p : H Y → H M . For a bundle functor E : ℱ ℳ m , n → ℱ ℳ with some weak conditions we prove non-existence of ℱ ℳ m , n -natural operators D transforming connections Γ on ( m , n ) -dimensional fibered manifolds Y → M into connections D ( Γ ) on E Y → M .

On g -natural conformal vector fields on unit tangent bundles

Mohamed Tahar Kadaoui Abbassi, Noura Amri (2021)

Czechoslovak Mathematical Journal

Similarity:

We study conformal and Killing vector fields on the unit tangent bundle, over a Riemannian manifold, equipped with an arbitrary pseudo-Riemannian g -natural metric. We characterize the conformal and Killing conditions for classical lifts of vector fields and we give a full classification of conformal fiber-preserving vector fields on the unit tangent bundle endowed with an arbitrary pseudo-Riemannian Kaluza-Klein type metric.

Bundle functors with the point property which admit prolongation of connections

W. M. Mikulski (2010)

Annales Polonici Mathematici

Similarity:

Let F:ℳ f →ℱℳ be a bundle functor with the point property F(pt) = pt, where pt is a one-point manifold. We prove that F is product preserving if and only if for any m and n there is an ℱ ℳ m , n -canonical construction D of general connections D(Γ) on Fp:FY → FM from general connections Γ on fibred manifolds p:Y → M.

Gauge natural constructions on higher order principal prolongations

Miroslav Doupovec, Włodzimierz M. Mikulski (2007)

Annales Polonici Mathematici

Similarity:

Let W m r P be a principal prolongation of a principal bundle P → M. We classify all gauge natural operators transforming principal connections on P → M and rth order linear connections on M into general connections on W m r P → M . We also describe all geometric constructions of classical linear connections on W m r P from principal connections on P → M and rth order linear connections on M.