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.
The original publication is available at www.sciencedirect.com.
© Toshiyuki Kobayashi