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The geometry of homogeneous submanifolds of hyperbolic space

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Abstract.

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.

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Received August 10, 1999; in final form November 23, 1999 / Published online March 12, 2001

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Di Scala, A., Olmos, C. The geometry of homogeneous submanifolds of hyperbolic space. Math Z 237, 199–209 (2001). https://doi.org/10.1007/PL00004860

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  • DOI: https://doi.org/10.1007/PL00004860

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