WEAK PROPER ACTIONS ON SOLVABLE HOMOGENEOUS SPACES

Abstract

Let H and K be closed connected subgroups of a connected, simply connected solvable Lie group G. We define the notion of weak and finite proper action of K on the homogeneous space X = G/H and prove that they are equivalent to the notion of (CI)-action of K on X in the sense of Kobayashi. We show also that the action of K on X is proper if and only if the solvable triple (G, H, K) has the (CI) property in both cases where one of those subgroups is maximal and where G is special.