INTRODUCTION TO A FEW METRIC ASPECTS OF FOLIATIONTHEORYREMI LANGEVIN (pp. 74-96)
Abstract.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 curvatureallows us to play the integral geometry games, that is slice with lines, planes etc. We can alsoconsider globally contact points with families of lines, planes etc. That way we obtain theoremsabout curvature functions defined by the leaves of our foliations.
Keywords: foliation, Reeb foliation, curvature, Gauss curvature, Gauss map, polar curves,isolated singularity.