Sur le groupe d'automorphismes des géométries paraboliques de rang 1
Frances, Charles
Annales scientifiques de l'École Normale Supérieure, Tome 40 (2007), p. 741-764 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{ASENS_2007_4_40_5_741_0,
     author = {Frances, Charles},
     title = {Sur le groupe d'automorphismes des g\'eom\'etries paraboliques de rang 1},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {40},
     year = {2007},
     pages = {741-764},
     doi = {10.1016/j.ansens.2007.07.003},
     mrnumber = {2382860},
     zbl = {1135.53016},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/ASENS_2007_4_40_5_741_0}
}

Frances, Charles. Sur le groupe d'automorphismes des géométries paraboliques de rang 1. Annales scientifiques de l'École Normale Supérieure, Tome 40 (2007) pp. 741-764. doi : 10.1016/j.ansens.2007.07.003. http://gdmltest.u-ga.fr/item/ASENS_2007_4_40_5_741_0/

[1] Biquard O., Métriques d'Einstein asymptotiquement symétriques, Astérisque 265 (2000). | Zbl 0967.53030

[2] Čap A., Two constructions with parabolic geometries, Rend. Circ. Mat. Palermo (2) Suppl. 79 (2006) 11-37. | MR 2287124 | Zbl 1120.53013

[3] Čap A., Schichl K., Parabolic geometries and canonical Cartan connections, Hokkaido Math. J. 29 (3) (2000) 453-505. | MR 1795487 | Zbl 0996.53023

[4] Cartan É., Les espaces généralisés, Notice sur les travaux scientifiques. Oeuvres Complètes, Partie I, vol. I, 1952, pp. 72-85.

[5] Cartan É., Sur la géométrie pseudo-conforme des hypersurfaces de deux variables complexes I, Ann. Math. Pures Appl. 11 (4) (1932) 17-90. | JFM 58.1256.03 | Zbl 0005.37304

[6] Cartan É., Sur la géométrie pseudo-conforme des hypersurfaces de deux variables complexes II, Ann. Scuola Norm. Sup. Pisa 1 (2) (1932) 333-354. | Numdam | MR 1556687 | Zbl 0005.37401

[7] Chern S.S., Moser J., Real hypersurfaces in complex manifolds, Acta Math. 133 (1974) 219-271. | MR 425155 | Zbl 0302.32015

[8] Ferrand J., Transformations conformes et quasi-conformes des variétés riemanniennes compactes, Mémoires Académie Royale de Belgique. Classe des Sciences 39 (5) (1971) 1-44. | MR 322739 | Zbl 0215.50902

[9] Ferrand J., The action of conformal transformations on a Riemannian manifold, Math. Ann. 304 (2) (1996) 277-291. | MR 1371767 | Zbl 0866.53027

[10] Frances C., Un théorème de rigidité pour certains plongements de géométries de Cartan, en préparation.

[11] Frances C., Sur les variétés lorentziennes dont le groupe conforme est essentiel, Math. Ann. 332 (1) (2005) 103-119. | MR 2139253 | Zbl 1085.53061

[12] Frances C., Tarquini C., Autour du théorème de Ferrand-Obata, Ann. Global Anal. Geom. 21 (1) (2002) 51-62. | Zbl 1005.53011

[13] Goldman W.M., Complex Hyperbolic Geometry, Oxford Mathematical Monographs. Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1999. | MR 1695450 | Zbl 0939.32024

[14] Kamada H., Nayatani S., Quaternionic analogue of CR geometry, Séminaire de Théorie Spectrale et Géométrie de Grenoble 19 (2001) 41-52. | Numdam | MR 1909075 | Zbl 1044.53032

[15] Knapp A.W., Lie Groups Beyond an Introduction, Progress in Mathematics, vol. 140, second ed., Birkhäuser, Boston, 2002. | MR 1920389 | Zbl 0862.22006

[16] Kobayashi S., Transformation Groups in Differential Geometry, Springer-Verlag, 1972. | MR 355886 | Zbl 0246.53031

[17] Kuiper N., On conformally flat spaces in the large, Ann. of Math. 50 (1949) 916-924. | MR 31310 | Zbl 0041.09303

[18] Lafontaine J., The theorem of Lelong-Ferrand and Obata, in: Conformal Geometry, Bonn, 1985/1986, Aspects Math., vol. E12, Vieweg, Braunschweig, 1988, pp. 93-103. | Zbl 0668.53022

[19] Lichnerowicz A., Sur les transformations conformes d'une variété riemannienne compacte, C. R. Acad. Sci. Paris 259 (1964) 697-700. | MR 166734 | Zbl 0126.37803

[20] Morimoto T., Geometric structures on filtered manifolds, Hokkaido Math. J. 22 (1993) 263-347. | MR 1245130 | Zbl 0801.53019

[21] Obata M., The conjectures on conformal transformations of Riemannian manifolds, J. Differential Geometry 6 (1971/72) 247-258. | MR 303464 | Zbl 0236.53042

[22] Schmidt B., A new definition of conformal and projective infinity of space-times, Comm. Math. Phys. 36 (1) (1974) 73-90. | Zbl 0282.53042

[23] Schoen R., On the conformal and CR automorphism groups, Geom. Funct. Anal. 5 (2) (1995) 464-481. | MR 1334876 | Zbl 0835.53015

[24] Sharpe R.W., Differential Geometry. Cartan's generalization of Klein's Erlangen program, Graduate Texts in Mathematics, vol. 166, Springer-Verlag, New York, 2000. | MR 1453120 | Zbl 0876.53001

[25] Sternberg S., Lectures on Differential Geometry, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1964. | MR 193578 | Zbl 0129.13102

[26] Tanaka N., On non-degenerate real hypersurfaces, graded Lie algebras, and Cartan connections, Japan J. Math. 2 (1976) 131-190. | MR 589931 | Zbl 0346.32010

[27] Tanaka N., On the equivalence problem associated with simple graded Lie algebras, Hokkaido Math. J. 8 (1979) 23-84. | MR 533089 | Zbl 0409.17013

[28] Thurston W., Three Dimensional Geometry and Topology. Vol. 1, Princeton University Press, 1997, Edited by Silvio Levy. | MR 1435975 | Zbl 0873.57001

[29] Webster S.M., On the transformation group of a real hypersurface, Trans. Amer. Math. Soc. 231 (1977) 179-190. | MR 481085 | Zbl 0368.57013