  We show that there is no positive loop inside the component of a fiber in the
space of Legendrian embeddings in the contact manifold $ST^*M$, provided that
the universal cover of $M$ is $\RM^n$. We consider some related results in the
space of one-jets of functions on a compact manifold. We give an application to
the positive isotopies in homogeneous neighborhoods of surfaces in a tight
contact 3-manifold.
