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Complétude des métriques lorentziennes de\(\mathbb{T}^2 \) et difféomorphismes du cercle

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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\(\mathcal{G}\).

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Bibliographie

  • [C] Carrière, Y.,—Autour de la conjecture de L. Markus sur les variétés affines, Invent. Math.95 (1989) 615–628.

    Google Scholar 

  • [FGH] Fried, D., Goldman, W., Hirsch, M.—Affine manifolds with nilpotent holonomy, Comment. Math. Helv.56 (1981) 487–523.

    Google Scholar 

  • [Gl] Gluck, H.—Dynamical behavior of geodesics fields, Proceedings of the International conference at Northwestern, Lecture Notes in Mathematics 819, pp. 190–215 (1979).

    Google Scholar 

  • [G] Godbillon, C.—Dynamical systems on surfaces, Universitext, Springer Verlag, Berlin Heidelberg New York (1983)

    Google Scholar 

  • [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.

    Google Scholar 

  • [HH] Hector, G., Hirsch, U.—Introduction to the geometry of foliations, Part A: Aspects of Mathematics, Vieweg, Braunschweig (1981).

    Google Scholar 

  • [K] Kamishima, Y.—Completeness of Lorentz manifolds, J. Diff. Geom.37 (1993) 569–601.

    Google Scholar 

  • [Kn] Kneser, H.—Reguläre Kurvenscharen auf den Ringflächen, Math. Annalen91 (1924) 135–154.

    Google Scholar 

  • [L1] Lafuente, J.—A geodesic completeness theorem for locally symmetric Lorentz manifolds, Revista Matemática de la Universidad Complutense de Madrid1 (1988) 101–110.

    Google Scholar 

  • [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).

    Google Scholar 

  • [O] O'Neill, B.—Semi-Riemannian Geometry, Academic Press, New York (1983).

    Google Scholar 

  • [RS1] Romero, A., Sánchez, M.—On the completeness of geodesics obtained as a limit, J. Math. Phys.34 (1993) 3768–74.

    Google Scholar 

  • [RS2] Romero, A., Sánchez, M.—New properties and examples of incomplete Lorentzian tori, J. Math. Rhys.35 (1994) 1992–97.

    Google Scholar 

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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

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  • DOI: https://doi.org/10.1007/BF01321310

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