Abstract:
It is proved that for a Riemannian manifold M with nonpositive sectional curvature and finite volume the space of directions at each point in which geodesic rays avoid a sufficiently small neighborhood of a fixed rank 1 vector v∈UM looks very much like a generalized Sierpinski carpet. We also show for nonpositively curved manifolds M with dim M≥ 3 the existence of proper closed flow invariant subsets of the unit tangent bundle UM whose footpoint projection is the whole of M.
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Received: 6 July 2000 / Revised version: 11 October 2001
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Buyalo, S., Schroeder, V. Invariant subsets of rank 1 manifolds. manuscripta math. 107, 73–88 (2002). https://doi.org/10.1007/s002290100225
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DOI: https://doi.org/10.1007/s002290100225