×

zbMATH — the first resource for mathematics

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.)
PDF BibTeX XML Cite
Full Text: DOI