Abstract
Let\(\mathcal{F}\) and\(\mathcal{G}\) the foliations by the null geodesics of some lorentzian metricg on the torus\(\mathbb{T}^2 \). We analyse how geodesic completeness properties ofg are related to the dynamics of\(\mathcal{F}\) and\(\mathcal{G}\).
Similar content being viewed by others
Bibliographie
[C] Carrière, Y.,—Autour de la conjecture de L. Markus sur les variétés affines, Invent. Math.95 (1989) 615–628.
[FGH] Fried, D., Goldman, W., Hirsch, M.—Affine manifolds with nilpotent holonomy, Comment. Math. Helv.56 (1981) 487–523.
[Gl] Gluck, H.—Dynamical behavior of geodesics fields, Proceedings of the International conference at Northwestern, Lecture Notes in Mathematics 819, pp. 190–215 (1979).
[G] Godbillon, C.—Dynamical systems on surfaces, Universitext, Springer Verlag, Berlin Heidelberg New York (1983)
[GL] Guediri, M., Lafontaine, J.—Sur la complétude des variétés pseudoriemanniennes, A paraître au J. of Geom. and Physic (1993).
[H] Herman, M.—Sur la conjugaison des difféomorphismes du cercle à des rotations, Pub. Math. I.H.E.S.49 (1979) 5–234.
[HH] Hector, G., Hirsch, U.—Introduction to the geometry of foliations, Part A: Aspects of Mathematics, Vieweg, Braunschweig (1981).
[K] Kamishima, Y.—Completeness of Lorentz manifolds, J. Diff. Geom.37 (1993) 569–601.
[Kn] Kneser, H.—Reguläre Kurvenscharen auf den Ringflächen, Math. Annalen91 (1924) 135–154.
[L1] Lafuente, J.—A geodesic completeness theorem for locally symmetric Lorentz manifolds, Revista Matemática de la Universidad Complutense de Madrid1 (1988) 101–110.
[L2] Lafuente, J.—On the limit set of an incomplete geodesic of a lorentzian torus, XV Jornadas Luso-Espagnolas Univesidad de Evora (1991).
[MS] de Melo, W., van Strien, S.—One-dimensional dynamics, Ergebnisse Math. 25, Springer Verlag, Berlin Heidelberg New York (1993).
[O] O'Neill, B.—Semi-Riemannian Geometry, Academic Press, New York (1983).
[RS1] Romero, A., Sánchez, M.—On the completeness of geodesics obtained as a limit, J. Math. Phys.34 (1993) 3768–74.
[RS2] Romero, A., Sánchez, M.—New properties and examples of incomplete Lorentzian tori, J. Math. Rhys.35 (1994) 1992–97.
Author information
Authors and Affiliations
About this article
Cite this article
Carrière, Y., Rozoy, L. Complétude des métriques lorentziennes de\(\mathbb{T}^2 \) et difféomorphismes du cercle. Bol. Soc. Bras. Mat 25, 223–235 (1994). https://doi.org/10.1007/BF01321310
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01321310