The geometry of homogeneous submanifolds of hyperbolic space

DI SCALA, ANTONIO J.; OLMOS, CARLOS

MATHEMATISCHE ZEITSCHRIFT

SPRINGER

Lugar: Berlin; Año: 2001 vol. 237 p. 199 - 209

0025-5874

We prove, in a purely geometric way, that there are no connected irreducible proper subgroups of SO(N,1). Moreover, a weakly irreducible subgroup of SO(N,1) must either act transitively irreducible subgroup of SO(N,1) must either act transitively on the hyperbolic space or on a horosphere. This has obvious consequences for Lorentzian holonomy and in particular explains clasification results of Marcel Berger´s list (e.g. the fact that an irreducible Lorentzian locally symmetric space has constant curvatures). We also prove that a minimal homogeneous submanifold of hyperbolic space must be totally-geodesic.