Special tangent valued forms and the Frölicher-Nijenhuis bracket

Antonella Cabras; Ivan Kolář

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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

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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

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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...