T. Kobayashi,
On discontinuous groups acting on homogeneous spaces with noncompact isotropy subgroups,
J. Geom. Physics 12 (1993), 133-144..
Let G be a Lie group and H a closed subgroup. The action of a discrete subgroup Γ of G on G/H is not always properly discontinuous if H is non-compact. If the action of Γ is properly discontinuous, then Γ is called a discontinuous group acting on G/H. If G/H is of reductive type, it is known that there are no infinite discontinuous groups acting on G/H (called Calabi-Markus phenomenon) iff R-rank G = R-rank H. For a better understanding of discontinuous groups we are thus interested in cases (i) where G/H is non-reductive, and (ii) where G/H is of reductive type with R-rank G = R-rank H + 1. In this paper we consider the Calabi-Markus phenomenon in solvable cases of type (i). We also study discontinuous groups of reductive group manifolds for case (ii) and generalize a result of Kulkarni-Raymond to higher dimensions.

[ preprint version(dvi) | ScienceDirect | ZMath | related papers ]

The original publication is available at www.sciencedirect.com.

Home EnHome Jp

© Toshiyuki Kobayashi