Displaying similar documents to “Special tangent valued forms and the Frölicher-Nijenhuis bracket”

Prolongation of tangent valued forms to Weil bundles

Antonella Cabras, Ivan Kolář (1995)

Archivum Mathematicum

Similarity:

We prove that the so-called complete lifting of tangent valued forms from a manifold M to an arbitrary Weil bundle over M preserves the Frölicher-Nijenhuis bracket. We also deduce that the complete lifts of connections are torsion-free in the sense of M. Modugno and the second author.

Flow prolongation of some tangent valued forms

Antonella Cabras, Ivan Kolář (2008)

Czechoslovak Mathematical Journal

Similarity:

We study the prolongation of semibasic projectable tangent valued k -forms on fibered manifolds with respect to a bundle functor F on local isomorphisms that is based on the flow prolongation of vector fields and uses an auxiliary linear r -th order connection on the base manifold, where r is the base order of F . We find a general condition under which the Frölicher-Nijenhuis bracket is preserved. Special attention is paid to the curvature of connections. The first order jet functor and...

Prolongation of pairs of connections into connections on vertical bundles

Miroslav Doupovec, Włodzimierz M. Mikulski (2005)

Archivum Mathematicum

Similarity:

Let F be a natural bundle. We introduce the geometrical construction transforming two general connections into a general connection on the F -vertical bundle. Then we determine all natural operators of this type and we generalize the result by IK̇olář and the second author on the prolongation of connections to F -vertical bundles. We also present some examples and applications.

On the iterated absolute differentiation on some functional bundles

Antonella Cabras, Ivan Kolář (1997)

Archivum Mathematicum

Similarity:

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.