First order jets of bundles over a manifold endowed with a sub- foliation

Abstract

Let (E, π, M) be a bundle over the manifold (M, F₁, F₂), where (F₁, F₂) is a subfoliation on M. We define (F₁, F₂)-1-jet manifold, J¹_F21π. If J¹π is the 1-jet manifold of π, then there is a diffeomorphism between J¹π and the total space of the fibre bundle J^t_F1π × _E J¹_F21π × _E J^l_F2 π, where J^t_F1π and J^l_F2π are the transversal 1-jet manifold and the leaf wise 1-jet manifold of the bundle π, with respect to foliations F₁ and F₂, respectively.