LOCALLY FREE ACTIONS OF RESOLUBLE GROUPS

Let G be a connected (n - 1)-dimensional Lie group and Omega a C-r (r greater than or equal to 2) locally free action of G on a compact n-dimensional manifold (n greater than or equal to 3). We assume that the Lie algebra of G contains a field Y such that the eigenvalues of ad(Y) are alpha(1),..., alpha(n-2), 0 with Re(alpha(i)) < 0. Then, we show that Phi is C-r-conjugated to a homogeneous action of G on H/Gamma where H is a Lie group containing H and Gamma a lattice of H. We provide many examples, related to Anosov theory.