Prolongations of G-structures related to Weil bundles and some applications

Abstract

Let M be a smooth manifold of dimension m ≥ 1 and P be a G-structure on M, where G is a Lie subgroup of linear group GL(m). In [8], it has been dened the prolongations of G-structures related to tangent functor of higher order and some properties have been established. The aim of this paper is to generalize these prolongations to a Weil bundles. More precisely, we study the prolongations of G-structures on a manifold M, to its Weil bundle ΤᴬM (A is a Weil algebra) and we establish some properties. In particular, we characterize the canonical tensor elds induced by the A-prolongation of some classical G-structures.