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Geometric & Functional Analysis GAFA

, Volume 4, Issue 1, pp 37–51 | Cite as

Quadratic divergence of geodesics in CAT(0) spaces

  • S. M. Gersten
Article

Abstract

A finite CAT(0) 2-complexX is produced whose universal cover possesses two geodesic rays which diverge quadratically and such that no pair of rays diverges faster than quadratically. This example shows that an aphorism in Riemannian geometry, that predicts that in nonpositive curvature nonasymptotic geodesic rays either diverge exponentially or diverge linearly, does not hold in the setting of CAT(0) complexes. The fundamental group ofX is that of a compact Riemannian manifold with totally geodesic boundary and nonpositive sectional curvature.

Keywords

Riemannian Manifold Fundamental Group Sectional Curvature Universal Cover Riemannian Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • S. M. Gersten
    • 1
  1. 1.Mathematics Dept.University of UtahSalt Lake CityUSA

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