HOROSPHERICAL FLOWS ON HOMOGENEOUS SPACES OF FINITE VOLUME

Horospherical flows are considered on homogeneous spaces of finite volume. An ergodic decomposition of such flows is constructed in explicit form, and it is proved that the horospherical orbits have constant dimension. A conjecture of Raghunathan is proved for the closure of the orbits of horospherical flows under the additional assumption that the homogeneous space is compact.