Functorial prolongations of some functional bundles

We discuss two kinds of functorial prolongations of the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base. We study the prolongation of vector fields in both cases and we prove that the bracket is preserved. Our proof is based on several new results concerning the finite dimensional Weil bundles

On the geometry of vertical Weil bundles

summary:We describe some general geometric properties of the fiber product preserving bundle functors. Special attention is paid to the vertical Weil bundles. We discuss namely the flow natural maps and the functorial prolongation of connections

On special types of nonholonomic contact elements

AbstractOur starting point has been a recent clarification of the role of semiholonomic contact elements in the theory of submanifolds of Cartan geometries, Kolář and Vitolo (2010) [5]. We deduce some further properties of the iterated contact elements by using the general concept of contact (n,F)-element for a regular subcategory F of the category of nonholonomic r-jets. Special attention is paid to the incidence relation of contact F-elements of different dimensions