2000/09/22 by Francois Labourie, Labourie, Francois
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG
paper · pdf · doi:10.48550/arxiv.math/0009205
6 figures
arxiv created 2000/09/22 · arxiv updated 2009/11/30
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.