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On the existence of prolongation of connections

Miroslav Doupovec, Włodzimierz M. Mikulski (2006)

Czechoslovak Mathematical Journal

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

On the fiber product preserving gauge bundle functors on vector bundles

Włodzimierz M. Mikulski (2003)

Annales Polonici Mathematici

We present a complete description of all fiber product preserving gauge bundle functors F on the category m of vector bundles with m-dimensional bases and vector bundle maps with local diffeomorphisms as base maps. Some corollaries of this result are presented.

On the functorial prolongations of principal bundles

Ivan Kolář, Antonella Cabras (2006)

Commentationes Mathematicae Universitatis Carolinae

We describe the fundamental properties of the infinitesimal actions related with functorial prolongations of principal and associated bundles with respect to fiber product preserving bundle functors. Our approach is essentially based on the Weil algebra technique and an original concept of weak principal bundle.

On the geometry of vertical Weil bundles

Ivan Kolář (2014)

Archivum Mathematicum

We describe some general geometric properties of the fiber product preserving bundle functors. Special attention is paid to the vertical Weil bundles. We discuss namely the flow natural maps and the functorial prolongation of connections.

On the Helmholtz operator of variational calculus in fibered-fibered manifolds

W. M. Mikulski (2007)

Annales Polonici Mathematici

A fibered-fibered manifold is a surjective fibered submersion π: Y → X between fibered manifolds. For natural numbers s ≥ r ≤ q an (r,s,q)th order Lagrangian on a fibered-fibered manifold π: Y → X is a base-preserving morphism λ : J r , s , q Y d i m X T * X . For p= max(q,s) there exists a canonical Euler morphism ( λ ) : J r + s , 2 s , r + p Y * Y d i m X T * X satisfying a decomposition property similar to the one in the fibered manifold case, and the critical fibered sections σ of Y are exactly the solutions of the Euler-Lagrange equation ( λ ) j r + s , 2 s , r + p σ = 0 . In the present paper, similarly...

On the iterated absolute differentiation on some functional bundles

Antonella Cabras, Ivan Kolář (1997)

Archivum Mathematicum

We deduce further properties of connections on the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base, which we introduced in [2]. In particular, we define the vertical prolongation of such a connection, discuss the iterated absolute differentiation by means of an auxiliary linear connection on the base manifold and prove the general Ricci identity.

On the jets of foliation respecting maps

Miroslav Doupovec, Ivan Kolář, Włodzimierz M. Mikulski (2010)

Czechoslovak Mathematical Journal

Using Weil algebra techniques, we determine all finite dimensional homomorphic images of germs of foliation respecting maps.

Currently displaying 41 – 60 of 77