Geometriae Dedicata

, Volume 118, Issue 1, pp 185–208 | Cite as

Connecting Geodesics and Security of Configurations in Compact Locally Symmetric Spaces

  • Eugene Gutkin
  • Viktor Schroeder


A pair of points in a Riemannian manifold makes a secure configuration if the totality of geodesics connecting them can be blocked by a finite set. The manifold is secure if every configuration is secure. We investigate the security of compact, locally symmetric spaces.


connecting geodesics blocking points restricted horocycle exponential map maximal flat restricted shadow singular configuration 

Mathematics Subject Classification (2000)

53C22 53C35 37D40 


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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.University of California and IMPARio de JaneiroBrasil
  2. 2.Department of MathematicsUniversity of ZürichZürichSwitzerland

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