Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-23T19:22:16.097Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1] Charette, V., Proper Actions of Discrete Groups in 2 + 1 Spacetime. Doctoral dissertation, University of Maryland, 2000.Google Scholar
[2] Drumm, T., Fundamental polyhedra for Margulis space-times. Doctoral Dissertation, University of Maryland, 1990.Google Scholar
[3] Drumm, T., Fundamental polyhedra for Margulis space-times. Topology (4) 31 (1992), 677–683.Google Scholar
[4] Margulis, G. A., Free properly discontinuous groups of affine transformations. Dokl. Akad. Nauk SSSR 272 (1983), 937–940.Google Scholar
[5] Margulis, G. A., Complete affine locally flat manifolds with a free fundamental group. J. Soviet Math. 134 (1987), 129–134 Google Scholar