Consider a closed, smooth manifold M of non-positive curvature. Write p:UM→M for the unit tangent bundle over M and let > denote the subset consisting of all vectors of higher rank. This subset is closed and invariant under the geodesic flow on UM. We define the structured dimension s-dim > which, essentially, is the dimension of the set p( > ) of base points of > . The main result of this paper holds for manifolds with s-dim >
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