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Sur les variétés lorentziennes dont le groupe conforme est essentiel

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Nous proposons de nombreuses constructions de variétés compactes lorentziennes pour lesquelles le groupe conforme ne préserve aucune mesure lisse. Ceci montre que le théorème de Ferrand-Obata ne se généralise pas au cadre lorentzien.

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References

  1. Alekseevski, D.: Selfsimilar lorentzian manifolds. Ann. Global Anal. Geom. 3, 59–84 (1985)

    Article  Google Scholar 

  2. D’Ambra, G., Gromov, M.: Lectures on transformation groups: geometry and dynamics. Surveys in differential geometry (Cambridge, MA, 1990), Lehigh Univ., Bethlehem, PA, 19–111 (1991)

  3. Benoist, Y.: Propriétés asymptotiques des groupes linéaires. Geom. Funct. Anal. 7, 1–47 (1997)

    Google Scholar 

  4. Cahen, M., Kerbrat, Y.: Domaines symétriques des quadriques projectives. J. Math. Pures Appl. 62(9), 327–348 (1983)

    Google Scholar 

  5. de la Harpe, P.: Free groups in linear groups. Enseign. Math. 29(2), 129–144 (1983)

    Google Scholar 

  6. Ferrand, J.: Transformations conformes et quasiconformes des variétés riemanniennes; application à la démonstration d’une conjecture de A. Lichnerowicz. C. R. Acad. Sci. Paris Sér. A-B 269 (1969)

  7. Frances, C.: Géométrie et dynamique lorentziennes conformes. Thèse. 2002. http://www.umpa.ens-lyon.fr/~cfrances/

  8. Frances, C.: Lorentzian Kleinian groups. preprint. http://www.umpa.ens-lyon.fr/~cfrances/

  9. Frances, C., Tarquini, C.: Autour du théorème de Ferrand-Obata. Ann. Global Anal. Geom. 21, 51–62 (2002)

    Article  Google Scholar 

  10. Hawking, S.W., Ellis, G.F.R.: The large scale structure of space-time. Cambridge Monographs on Mathematical Physics, No. 1. Cambridge University Press, London-New York, 1973

  11. Iozzi, A., Witte, D.: Cartan-decomposition subgroups of SU(2,n). J. Lie Theory 11, 505–543 (2001)

    Google Scholar 

  12. Kühnel, W., Rademacher, H.B. Essential conformal fields in pseudo-Riemannian geometry. J. Math. Pures Appl. 74(9), 453–481 (1995)

    Google Scholar 

  13. Maskit, B.: Kleinian groups. Grundlehren der Mathematischen Wissenschaften , 287. Springer-Verlag, Berlin, 1988

  14. Obata, M.: The conjectures on conformal transformations of Riemannian manifolds. J. Differential Geometry 6, 247–258 (1971/72)

    Google Scholar 

  15. Penrose, R.: Conformal treatment of infinity. in: Relativité, Groupes et Topologie (Lectures, Les Houches, 1963 Summer School of Theoret. Phys., Univ. Grenoble) pp. 563–584, Gordon and Breach, New Ann. Global Anal. Geom. 21, 51–62York (2002)

  16. Seade, J., Verjovsky, A.: Higher dimensional complex Kleinian groups. Math. Ann. 322, 279–300 (2002)

    Article  Google Scholar 

  17. Thurston, W.: Three dimensional geometry and topology. Vol 1.- Princeton University Press, 1997. Edited by Silvio Levy

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Frances, C. Sur les variétés lorentziennes dont le groupe conforme est essentiel. Math. Ann. 332, 103–119 (2005). https://doi.org/10.1007/s00208-004-0619-x

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  • DOI: https://doi.org/10.1007/s00208-004-0619-x

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