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Geodesics in Margulis spacetimes

Published online by Cambridge University Press:  08 November 2011

WILLIAM M. GOLDMAN  and
FRANÇOIS LABOURIE
WILLIAM M. GOLDMAN
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA (email: wmg@math.umd.edu)
FRANÇOIS LABOURIE
Affiliation:
Laboratoire de Mathématiques, Université Paris-Sud, Orsay F-91405 Cedex; CNRS, Orsay cedex, F-91405, France (email: francois.labourie@math.u-psud.fr)
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Abstract

Let M3 be a Margulis spacetime whose associated complete hyperbolic surface Σ2 has a compact convex core. Generalizing the correspondence between closed geodesics on M3 and closed geodesics on Σ2, we establish an orbit equivalence between recurrent spacelike geodesics on M3 and recurrent geodesics on Σ2. In contrast, no timelike geodesic recurs in either forward or backward time.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 2: Daniel J. Rudolph – in Memoriam , April 2012 , pp. 643 - 651
Copyright
Copyright © Cambridge University Press 2011

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