Let $ X $ be a complete locally compact simply connected path-metric space which is non-positively curved in the sense of Busemann, namely that the distance function along pairs of geodesic segments is convex. Suppose $ \Gamma $ acts properly discontinuously cocompactly on $ X $. We show that either $ \Gamma $ is hyperbolic or else $ X $ contains a convex subset isometric to a minkowskian plane. If $ X $ is CAT(0), then in the second case, this plane must be euclidean.
Bull. London Math. Soc. 27 (1995) 575-584.