Universität Augsburg
Institut für Mathematik

On negatively curved compact (Riemannian) spaces, the space of geodesics splits up into families which converge exponentially fast in future resp. past, the stable/unstable leaves. These decompositions, called horospherical foliations, in general have a low degree of differentiability. In fact, smoothness has been proved to hold only for the locally symmetric hyperbolic model spaces.

We investigate a class of noncompact homogeneous spaces, which in general do not admit compact quotients, and prove an analogue: High regularity of the foliations only occurs for model spaces, the harmonic Damek-Ricci spaces (which include hyperbolic symmetric spaces).