Vertical and horizontal lifts of multivector fields and applications

Resumo

Let Q be a smoothmanifold of dimension n ≥ 1. In this paper,we define the vertical lift of multivector fields from Q to T Q and we give some applications in the Poisson geometry. In particular we describe the structure of singular foliation induced by the vertical lift of Poisson structures defined below. On the other hand, given a second order vector field on Q, we defined the horizontal lift of multivector fields from Q to TQ and we study some properties.