Non-existence of natural operators transforming connections on $Y \rightarrow M$ into connections on $FY\rightarrow Y$

Włodzimierz M. Mikulski

Displaying similar documents to “Non-existence of natural operators transforming connections on $Y \to M$ into connections on $F Y \to Y$ ”

On the existence of prolongation of connections

Miroslav Doupovec, Włodzimierz M. Mikulski (2006)

Czechoslovak Mathematical Journal

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We classify all bundle functors $G$ admitting natural operators transforming connections on a fibered manifold $Y \to M$ into connections on $G Y \to M$ . Then we solve a similar problem for natural operators transforming connections on $Y \to M$ into connections on $G Y \to Y$ .

Natural lifting of connections to vertical bundles

Kolář, Ivan, Mikulski, Włodzimierz M.

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One studies the flow prolongation of projectable vector fields with respect to a bundle functor of order $(r, s, q)$ on the category of fibered manifolds. As a result, one constructs an operator transforming connections on a fibered manifold $Y$ into connections on an arbitrary vertical bundle over $Y$ . It is deduced that this operator is the only natural one of finite order and one presents a condition on vertical bundles over $Y$ under which every natural operator in question has finite order. ...

On principal connection like bundles

Włodzimierz M. Mikulski (2014)

Czechoslovak Mathematical Journal

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Let $𝒫 ℬ_{m}$ be the category of all principal fibred bundles with $m$ -dimensional bases and their principal bundle homomorphisms covering embeddings. We introduce the concept of the so called $(r, m)$ -systems and describe all gauge bundle functors on $𝒫 ℬ_{m}$ of order $r$ by means of the $(r, m)$ -systems. Next we present several interesting examples of fiber product preserving gauge bundle functors on $𝒫 ℬ_{m}$ of order $r$ . Finally, we introduce the concept of product preserving $(r, m)$ -systems and describe all fiber product preserving...

Natural affinors on ${(J^{r, s, q} {(., ℝ^{1, 1})}_{0})}^{*}$

Włodzimierz M. Mikulski (2001)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let $r, s, q, m, n \in ℕ$ be such that $s \geq r \leq q$ . Let $Y$ be a fibered manifold with $m$ -dimensional basis and $n$ -dimensional fibers. All natural affinors on ${(J^{r, s, q} {(Y, ℝ^{1, 1})}_{0})}^{*}$ are classified. It is deduced that there is no natural generalized connection on ${(J^{r, s, q} {(Y, ℝ^{1, 1})}_{0})}^{*}$ . Similar problems with ${(J^{r, s} {(Y, ℝ)}_{0})}^{*}$ instead of ${(J^{r, s, q} {(Y, ℝ^{1, 1})}_{0})}^{*}$ are solved.

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.

Displaying similar documents to “Non-existence of natural operators transforming connections on Y → M into connections on F Y → Y ”

On the existence of prolongation of connections

Natural lifting of connections to vertical bundles

On principal connection like bundles

Natural affinors on ( J r , s , q ( . , ℝ 1 , 1 ) 0 ) *

Bundle functors with the point property which admit prolongation of connections

Displaying similar documents to “Non-existence of natural operators transforming connections on $Y \to M$ into connections on $F Y \to Y$ ”

Natural affinors on ${(J^{r, s, q} {(., ℝ^{1, 1})}_{0})}^{*}$