Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-16T10:52:05.918Z Has data issue: false hasContentIssue false
  • English
  • Français

Geodesic Flow on Ideal Polyhedra

Published online by Cambridge University Press:  20 November 2018

Charalambos Charitos  and
Georgios Tsapogas
Charalambos Charitos
Affiliation:
Agricultural University of Athens, Department of Mathematics, 75 Iera Odos, Athens 11855, Greece e-mail: gmat2xax@auadec.aua.ariadne-t.gr
Georgios Tsapogas
Affiliation:
University of the Aegean, Department of Mathematics,Karlovassi, Samos 83200, Greece e-mail: gtsap@aegean.gr
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.

In this work we study the geodesic flow on n-dimensional ideal polyhedra and establish classical (for manifolds of negative curvature) results concerning the distribution of closed orbits of the flow.

Keywords

57M2053C23
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 4 , 01 August 1997 , pp. 696 - 707
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Bourdon, M., Structure conforme au bord et flot géodésique d’un CAT(-1) espace. Enseign. Math. 41(1995), 63–102.Google Scholar
2. Bridson, M., Geodesics and curvature in metric simplicial complexes. In: Group Theory from a Geometrical Viewpoint, ICTP, Trieste, Italy, March 26–April 6, 1990. (eds. Ghys, E., Haefliger, A. and Verjovsky), 1991. 373–463.Google Scholar
3. Charitos, Ch., Closed geodesics on ideal polyhedra of dimension 2. Rocky Mountain J. Math. (1) 26(1996), 507–521.Google Scholar
4. Coornaert, M., Sur les groupes proprement discontinus d’isométries des espaces hyperboliques au sens de Gromov, Thèse U.L.P., Publication de l’IRMA.Google Scholar
5. Coornaert, M., Measures de Patterson-Sullivan sur le bord d’un espace hyperbolique au sens de Gromov. Pacific J. Math. (2) 159(1993), 241–270.Google Scholar
6. Coornaert, M., Delzant, T. and Papadopoulos, A., Géométrie et théorie des groupes. Lecture Notes in Math. 1441, Springer-Verlag, 1990.Google Scholar
7. Eberlein, P., Geodesic flows on negatively curved manifolds I. Ann. of Math. 95(1972), 151–170.Google Scholar
8. Eberlein, P. and O, B.’Neil, Visibility manifolds. Pacific J. Math. 46(1973), 45–109.Google Scholar
9. Gromov, M., Hyperbolic groups. In: Essays in Group Theory, MSRI Publ. 8, Springer Verlag, 1987. 75–263.Google Scholar
10. Paulin, F., Constructions of hyperbolic groups via hyperbolization of polyhedra. In: Group Theory from a Geometrical Viewpoint, ICTP, Trieste, Italy, March 26–April 6, 1990. (eds. Ghys, E. and Haefliger, A.), 1991.Google Scholar
11. Ratcliffe, J., Foundations of hyperbolic geometry, Graduate Texts in Math., Springer-Verlag, 1994.Google Scholar
12. Thurston, W.P., The Geometry and Topology of Three-manifolds, Lecture Notes, Princeton University, Princeton, New Jersey, 1979.Google Scholar