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Invariant subsets of rank 1 manifolds


Buyalo, S; Schroeder, V (2002). Invariant subsets of rank 1 manifolds. Manuscripta Mathematica, 107(1):73-88.

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.

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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1 citation in Web of Science®
1 citation in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:nonpositive sectional curvature; rank one vectors; invariant subsets
Language:English
Date:2002
Deposited On:29 Nov 2010 16:27
Last Modified:05 Apr 2016 13:25
Publisher:Springer
ISSN:0025-2611
Publisher DOI:10.1007/s002290100225
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1003.53031
http://www.ams.org/mathscinet-getitem?mr=1892773

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