Prolongation of projectable tangent valued forms
by
Ivan Kolář
Masaryk University, Czech Republic
Coauthors: Antonella Cabras (University of Florence)

Oral Communication

The Weil (or local) algebras represent a unified technique for investigating all product preserving bundle functors on the category of all manifolds, see e.g. [2]. The prolongation of tangent valued forms to an arbitrary Weil bundle was studied in [1]. W. Mikulski has recently deduced that all product preserving bundle functors on the category of all fibered manifolds are in bijection with the homomorphisms of Weil algebras, [3]. We shall discuss the prolongation of projectable tangent valued forms on fibered manifolds with respect to the product preserving bundle functors. Special attention will be paid to the Frölicher-Nijenhuis bracket. Some applications to the general connections and their torsions will be presented.

References

[1] A. Cabras, I. Kolar, Prolongation of tangent valued forms to Weil bundles, Archivum Math. (Brno) 31 (1995), 139-145.

[2] I. Kolar, P. W. Michor, J. Slovak, Natural Operations in Differential Geometry, Springer-Verlag, 1993.

[3] W. Mikulski, Product preserving bundle functors on fibered manifolds, Archivum Math.(Brno) 32 (1996), 307-316.

Date received: April 25, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadq-34.