The condition of non-commutativity of the squares of two vector fields in a nilpotent distribution

Abstract

In this Memory , we aim to define certain properties regarding the nilpotent distribution D = span{X,Y} in the space R n , This property determines the necessary condition for the Lie

bracket X 2 ,Y 2

̸= 0 . This result offers less computation and excellent description for the calcul of

X 2 ,Y 2

.