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Recurrent Geodesics in Flat Lorentz 3-Manifolds

Published online by Cambridge University Press:  20 November 2018

Virginie Charette ,
William M. Goldman  and
Catherine A. Jones
Virginie Charette
Affiliation:
Department of Mathematics University of Manitoba Winnipeg, Manitoba R3T 2N2, e-mail: charette@cc.umanitoba.ca
William M. Goldman
Affiliation:
Department of Mathematics University of Maryland College Park, Maryland 20742 USA, e-mail: wmg@math.umd.edu
Catherine A. Jones
Affiliation:
Department of Mathematics University of Maryland College Park, Maryland 20742 USA, e-mail: caj@math.umd.edu
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Abstract

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Let $M$ be a complete flat Lorentz 3-manifold $M$ with purely hyperbolic holonomy $\Gamma $. Recurrent geodesic rays are completely classified when $\Gamma $ is cyclic. This implies that for any pair of periodic geodesics ${{\gamma }_{1}}$, ${{\gamma }_{2}}$, a unique geodesic forward spirals towards ${{\gamma }_{1}}$ and backward spirals towards ${{\gamma }_{2}}$.

Keywords

57M5037B20geometric structures on low-dimensional manifoldsnotions of recurrence
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 3 , 01 September 2004 , pp. 332 - 342
Copyright
Copyright © Canadian Mathematical Society 2004

References

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