The Phase Space of k-Surfaces

Abstract

The purpose of this note is to provide an introduction to several articles concerning k-surfaces [7], [6], and more specially random ones [8]. Recall briefly that a k-surface is an immersed surface in a Riemannian manifold with curvature less than -1, such that the product of the principal curvatures is k, where k ∈ ]0,1[. Following these articles, we explain that k-surfaces possess (like geodesics) a “genuine” laminated phase space which has chaotic properties similar to those of the geodesic flow, and that, furthermore, the dynamics on this space can be coded, hence producing transversal measures.

L’auteur remercie l’Institut Universitaire de France.