Fixed points of isometries at infinity in homogeneous spaces (Q1103888)

Let M be a simply connected homogeneous Riemannian manifold of nonpositive curvature and let G be a solvable Lie group of isometries that acts simply and transitively on M. In this paper, we describe the set of fixed points of G at infinity and we classify all isometries defined by elements of G when M has no de Rham flat factor. Some results about the points at infinity that can be joined by a geodesic to a fixed point of G are obtained.