HARMONIC MAPS AND FUNDAMENTAL GROUPS OF NONPOSITIVELY CURVEDRIEMANNIAN MANIFOLDS

Using the theory of harmonic maps the authors discuss theproperties of the fundamental group of a complete nonpositivelycurved Riemannian manifold, and prove that the finitely generatedvirtual solvable subgroup of fundamental group of a completenonpositively curved Riemannian manifold either is a peripheralsubgroup of fundamental group or can be realized by animmersed totall geodesic closed flat manifold. It generalizessome results of Gromoll-Wolf, Lawson-Yan and Schoen-Yau.