Prolongation of projectable tangent valued forms

Antonella Cabras and Ivan Kolar

Address.  Antonella Cabras, Dipartamento di Matematica Applicata ``G. Sansone",
                 Via S. Marta 3, 50139 Firenze, Italy
                 I. Kolar, Department of Algebra and Geometry, Faculty of Science, Masaryk University,
                 Janackovo nam. 2a, 662 95 Brno, Czech Republic

Abstract.  First we deduce  some general properties  of product preserving
bundle functors  on the category of fibered manifolds. Then we
study the prolongation of projectable tangent valued forms with
respect to these functors and describe the complete lift of the
Fr\"olicher-Nijenhuis bracket. We also present  the coordinate
formula  for composition of semiholonomic jets.

AMSclassification.  53C05, 58A20.

Keywords. Projectable tangent  valued form, product  preserving bundle functor, jet, Weil bundle, Fr\"olicher-Nijenhuis bracket.