T. Kobayashi,

*On discontinuous groups acting on homogeneous spaces with
noncompact isotropy subgroups*,

J. Geom. Physics**12** (1993), 133-144..

J. Geom. Physics

LetGbe a Lie group andHa closed subgroup. The action of a discrete subgroup Γ ofGonG/His not always properly discontinuous ifHis non-compact. If the action of Γ is properly discontinuous, then Γ is called a discontinuous group acting onG/H. IfG/His of reductive type, it is known that there arenoinfinite discontinuous groups acting onG/H(called Calabi-Markus phenomenon) iffR-rankG=R-rankH. For a better understanding of discontinuous groups we are thus interested in cases (i) whereG/His non-reductive, and (ii) whereG/His of reductive type withR-rankG=R-rankH+ 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.

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© Toshiyuki Kobayashi