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Włodzimierz M. Mikulski

Displaying similar documents to “On 'special' fibred coordinates for general and classical connections”

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.

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 $H : ℳ f \to 𝒱 ℬ$ 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 $p : Y \to M$ into connections $D (Γ)$ on $H p : H Y \to H M$ . For a bundle functor $E : ℱ ℳ_{m, n} \to ℱ ℳ$ 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 $Y \to M$ into connections $D (Γ)$ on $E Y \to M$ .

Natural affinors on the (r,s,q)-cotangent bundle of a fibered manifold

J. Kurek, W. M. Mikulski (2004)

Annales Polonici Mathematici

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For natural numbers r,s,q,m,n with s ≥ r ≤ q we describe all natural affinors on the (r,s,q)-cotangent bundle $T^{r, s, q *} Y$ over an (m,n)-dimensional fibered manifold Y.

Lifting adapted connections from foliated manifolds to higher order adapted frame bundles

J. Kurek, W. M. Mikulski (2008)

Annales Polonici Mathematici

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Let (M,ℱ) be a foliated manifold. We describe all natural operators lifting ℱ-adapted (i.e. projectable in adapted coordinates) classical linear connections ∇ on (M,ℱ) into classical linear connections (∇) on the rth order adapted frame bundle $P^{r} (M, ℱ)$ .

A construction of a connection on $G Y \to Y$ from a connection on $Y \to M$ 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 $(r, s, q)$ , $s \geq r \leq q$ , 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 $Y \to M$ we construct a general connection $𝒢 (Γ, λ, Λ)$ on $G Y \to Y$ 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 $𝒢 (Γ, \nabla_{1}, \nabla_{2})$ on $G Y \to Y$ by means of auxiliary classical linear connections $\nabla_{1}$ on $M$ and $\nabla_{2}$ on $Y$ . In the case $G = J^{1}$ we determine all general connections...

Non-existence of natural operators transforming connections on $Y \to M$ into connections on $F Y \to Y$

Włodzimierz M. Mikulski (2005)

Archivum Mathematicum

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Under some weak assumptions on a bundle functor $F : F M_{m, n} \to F M$ we prove that there is no $F M_{m, n}$ -natural operator transforming connections on $Y \to M$ into connections on $F Y \to Y$ .

Natural maps depending on reductions of frame bundles

Ivan Kolář (2011)

Annales Polonici Mathematici

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We clarify how the natural transformations of fiber product preserving bundle functors on $ℱ ℳ_{m}$ can be constructed by using reductions of the rth order frame bundle of the base, $ℱ ℳ_{m}$ being the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps. The iteration of two general r-jet functors is discussed in detail.

Displaying similar documents to “On 'special' fibred coordinates for general and classical connections”

Bundle functors with the point property which admit prolongation of connections

Non-existence of some canonical constructions on connections

Natural affinors on the (r,s,q)-cotangent bundle of a fibered manifold

Lifting adapted connections from foliated manifolds to higher order adapted frame bundles

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

Non-existence of natural operators transforming connections on Y → M into connections on F Y → Y

Natural maps depending on reductions of frame bundles

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

Non-existence of natural operators transforming connections on $Y \to M$ into connections on $F Y \to Y$