  The main result is the construction of ergodic transversal measures of full
support on the space of all k-surfaces of a compact hyperbolic 3-manifold. This
space is a laminated space, each of its leaf being identified with a "complete"
k-surface, i.e. a surface of constant (extrinsic) curvature k, where k belongs
to ]0,1[. Elsewhere, this space has been shown to have chaotic properties
mimicking those of the geodesic flow. This construction is achieved through a
coding of the space.

Differential Geometry