The geometry of homogeneous submanifolds of hyperbolic space. (English) Zbl 0997.53051

Di Scala, Antonio J.; Olmos, Carlos

Math. Z. 237, No. 1, 199-209 (2001).

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.

Reviewer: Karin Riives (Tartu)

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.)