Prolongation of second order connections to vertical Weil bundles

Antonella Cabras and Ivan Kolar

Address. Antonella Cabras, Dipartimento di Matematica Applicata ``G. Sansone", Via S. Marta 3, 50139 Firenze, ITALY

Ivan Kolar, Department of Algebra and Geometry, Faculty of Science, Masaryk University, Janackovo nam. 2a, 662 95 Brno, CZECH REPUBLIC

E-mail: cabras@dma.unifi.it

             kolar@math.muni.cz

Abstract. We study systematically the prolongation of second order connections in the sense of C. Ehresmann from a fibered manifold into its vertical bundle determined by a Weil algebra $A$. In certain situations we deduce new properties of the prolongation of first order connections. Our original tool is a general concept of a $B$-field for another Weil algebra $B$ and of its $A$-prolongation.

AMSclassification. 58A20, 53C05

Keywords. Non-holonomic jet, Weil bundle, Weil field, second order connection, prolongation of connections