INTRODUCTION TO A FEW METRIC ASPECTS OF FOLIATION THEORY

Foliations can be studied from a dynamical viewpoint, folowing holonomy maps. Here we focus on the geometry of the leaves of codimension one foliations of surfaces of 3- manifolds of constant curvature. The fact that the ambient space is of constant curvature allows us to play the integral geometry games, that is slice with lines, planes etc. We can also consider globally contact points with families of lines, planes etc. That way we obtain theorems about curvature functions defined by the leaves of our foliations.