Prolongation of second order connections to vertical Weil bundles

Antonella Cabras and Ivan Kolar

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