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The geometry of homogeneous submanifolds of hyperbolic space. (English) Zbl 0997.53051
It is proved that there are no connected irreducible proper subgroups of $$\text{SO}(N,1)$$ and that a weakly irreducible subgroup of $$\text{SO}(N,1)$$ must either act transitively on the hyperbolic space or on a horosphere. It is shown that a minimal homogeneous submanifold of hyperbolic space must be totally geodesic.

##### MSC:
 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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