On jet like bundles of vector bundles

Abstract

We describe completely the so called jet like functors of a vector bundle E over an m-dimensional manifold M, i.e. bundles FE over M canonically depending on E such that F(E-1 x(M) E-2) = FE1 x(M) FE2 for any vector bundles E-l and E-2 over M. Then we study how a linear vector field on E can induce canonically a vector field on FE.We describe completely the so called jet like functors of a vector bundle E over an m-dimensional manifold M, i.e. bundles FE over M canonically depending on E such that F(E-1 x(M) E-2) = FE1 x(M) FE2 for any vector bundles E-l and E-2 over M. Then we study how a linear vector field on E can induce canonically a vector field on FE.