FOLIATIONS FORMED BY K-ORBITS OF MAXIMAL DIMENSION OF SOME MD5-GROUPS

Abstract

In this paper we consider some MD5-groups and MD5-algebras, i.e., five-dimensional solvable Lie algebras and groups such that their orbits in the co-adjoint representation ( K-orbits ) are orbits of dimension zero or maximal dimension. We describe the geometry of K-orbits of MD5groups. The foliations formed by K-orbits of maximal dimension of these MD5-groups and their measurability are also presented in the paper.