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...

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

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