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Flow prolongation of some tangent valued forms

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Abstract

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 the tangent functor are discussed in detail. Next we clarify how this prolongation procedure can be extended to arbitrary projectable tangent valued k-forms in the case F is a fiber product preserving bundle functor on the category of fibered manifolds with m-dimensional bases and local diffeomorphisms as base maps.

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Authors and Affiliations

  1. Dipartimento di Matematica Applicata “G. Sansone”, Via S.Marta 3, 501 39, Firenze, Italy

    Antonella Cabras

  2. Department of Algebra and Geometry, Faculty of Science, Masaryk University, Janáčkovo nám. 2a, 662 95, Brno, Czech Republic

    Ivan Kolář

Authors
  1. Antonella Cabras
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  2. Ivan Kolář
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Correspondence to Antonella Cabras.

Additional information

This work was done during the visit of I. Kolář at Dipartimento di Matematica Applicata “G. Sansone”, Università di Firenze, supported by the University of Florence. The second author was also supported by a grant of the GAČR No. 201/05/0523.

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Cabras, A., Kolář, I. Flow prolongation of some tangent valued forms. Czech Math J 58, 493–504 (2008). https://doi.org/10.1007/s10587-008-0031-x

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  • DOI: https://doi.org/10.1007/s10587-008-0031-x

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