  We classify semi-Riemannian submersions with connected totally geodesic
fibres from a real pseudo-hyperbolic space onto a semi-Riemannian manifold
under the assumption that the dimension of the fibres is less than or equal to
three and the metrics induced on fibres are negative definite. Also, we obtain
the classification of semi-Riemannian submersions with connected complex
totally geodesic fibres from a complex pseudo-hyperbolic space onto a
semi-Riemannian manifold under the assumption that the dimension of the fibres
is less than or equal to two and the metric induced on fibres are negative
definite. We prove that there are no semi-Riemannian submersions with connected
quaternionic fibres from a quaternionic pseudo-hyperbolic space onto a
Riemannian manifold.
