Displaying similar documents to “Gauge natural prolongation of connections”

Gauge natural constructions on higher order principal prolongations

Miroslav Doupovec, Włodzimierz M. Mikulski (2007)

Annales Polonici Mathematici

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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.

Bundle functors with the point property which admit prolongation of connections

W. M. Mikulski (2010)

Annales Polonici Mathematici

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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.

On "special" fibred coordinates for general and classical connections

Włodzimierz M. Mikulski (2010)

Annales Polonici Mathematici

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Using a general connection Γ on a fibred manifold p:Y → M and a torsion free classical linear connection ∇ on M, we distinguish some “special” fibred coordinate systems on Y, and then we construct a general connection ℱ ˜ ( Γ , ∇ ) on Fp:FY → FM for any vector bundle functor F: ℳ f → of finite order.

Non-existence of some canonical constructions on connections

Włodzimierz M. Mikulski (2003)

Commentationes Mathematicae Universitatis Carolinae

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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 .

Classification of principal connections naturally induced on W 2 P E

Jan Vondra (2008)

Archivum Mathematicum

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We consider a vector bundle E → M and the principal bundle P E of frames of E . Let K be a principal connection on P E and let Λ be a linear connection on M . We classify all principal connections on W 2 P E = P 2 M × M J 2 P E naturally given by K and Λ .