no. 2
Feuilletages conformes
Tarquini, Cédric1
1 U.M.P.A., École Normale Supérieure de Lyon, allée d'Italie, 69364 Lyon cedex 07 (France)
Annales de l'Institut Fourier, Tome 54 (2004) no. 2, pp. 453-480.

Dans cet article nous montrons que tout feuilletage conforme, transversalement analytique, de codimension supérieure ou égale à trois sur une variété compacte connexe est transversalement Möbius ou riemannien. Ce théorème peut être vu comme une généralisation, transversalement à un feuilletage, du théorème Ferrand-Obata.

In this article we prove that every conformal foliation, transversely analytic, of codimension at most three on a compact connected manifold is either transversely Möbius or Riemannian. This theorem can be seen as a generalisation of the Ferrand-Obata theorem transversely to a foliation.

DOI : 10.5802/aif.2025
Classification : 53C12, 58H05, 53A20
Mot clés : feuilletages, pseudogroupes, géométrie différentielle conforme.
Keywords: foliations, pseudogroups, conformal differential geometry.

Tarquini, Cédric 1

1 U.M.P.A., École Normale Supérieure de Lyon, allée d'Italie, 69364 Lyon cedex 07 (France) 
@article{AIF_2004__54_2_453_0,
     author = {Tarquini, C\'edric},
     title = {Feuilletages conformes},
     journal = {Annales de l'Institut Fourier},
     pages = {453--480},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {54},
     number = {2},
     year = {2004},
     doi = {10.5802/aif.2025},
     zbl = {1064.53014},
     language = {fr},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2025/}
}
TY  - JOUR
AU  - Tarquini, Cédric
TI  - Feuilletages conformes
JO  - Annales de l'Institut Fourier
PY  - 2004
SP  - 453
EP  - 480
VL  - 54
IS  - 2
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.2025/
DO  - 10.5802/aif.2025
LA  - fr
ID  - AIF_2004__54_2_453_0
ER  - 
%0 Journal Article
%A Tarquini, Cédric
%T Feuilletages conformes
%J Annales de l'Institut Fourier
%D 2004
%P 453-480
%V 54
%N 2
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.2025/
%R 10.5802/aif.2025
%G fr
%F AIF_2004__54_2_453_0
Tarquini, Cédric. Feuilletages conformes. Annales de l'Institut Fourier, Tome 54 (2004) no. 2, pp. 453-480. doi : 10.5802/aif.2025. https://aif.centre-mersenne.org/articles/10.5802/aif.2025/

[1] V. Arnold Chapitres supplémentaires de la théorie des équations différentielles ordinaires, Moscou, 1980 | MR | Zbl

[2] T. Asuke On transversaly flat conformal foliations with good measures II, Hiroshima Math. J, Volume 28 (1998), pp. 523-525 | MR | Zbl

[3] M. Belliart On the dynamics of certain actions of free groups on closed real analytic manifolds, Commentarii Mathematici Helvetici, Volume 77 (2002), pp. 524-548 | MR | Zbl

[4] M. Brunella On transversely holomorphic flows I, Inventiones Mathematicae, Volume 126 (1996) no. 2, pp. 265-279 | MR | Zbl

[5] J. Ferrand Transformations conformes et quasi conformes des variétés riemanniennes : application à la démonstration d'une conjecture de A. Lichnerowicz, C.R.Acad.Sci. Paris, Série A, Volume 269 (1969), pp. 583-586 | Zbl

[6] J. Ferrand The action of conformal transformations on a Riemannian manifold, Mathematische Annalen, Volume 304 (1996), pp. 277-291 | MR | Zbl

[7] C. Frances; C. Tarquini Autour du théorème de Ferrand-Obata, Annals of Global Analysis and Geometry, Volume 21 (2002), pp. 51-62 | MR | Zbl

[8] S. Gallot; D. Hulin; J. Lafontaine Riemannian Geometry, Universitext, Springer-Verlag, Berlin-Heidelberg, 1987-1990 | MR | Zbl

[9] É. Ghys Flots transversalement affines et tissus feuilletés, Mémoire de la Société Mathématiques de France (N.S), Volume 46 (1991), pp. 123-150 | Numdam | MR | Zbl

[10] É. Ghys On transversaly holomorphic flows II, Inventiones Mathematicae, Volume 126 (1996), pp. 281-286 | MR | Zbl

[11] A. Haefliger Pseudo-groupes of locales isometries, Proceeding Vth Coll. in Diff. Geom, Volume 131 (1985), pp. 174-197 | Zbl

[12] M. Kellum Uniform lipschitz distortion, invariant measures and foliations, Geometric study of foliations (Tokyo, 1993) (1994), pp. 313-326 | MR

[13] S. Kobayashi Transformation groups in differential geometry, Springer-Verlag, Berlin-Heidelberg-New York, 1972 | MR | Zbl

[14] M. Obata The conjectures on conformal transformations of Riemannian manifolds, J. Differential Geom, Volume 6 (1971), pp. 247-258 | MR | Zbl

[15] R. Palais On the existence of slices for actions of non-compact Lie groups, Annals of Mathematics, Volume 73 (1961) no. 2, pp. 295-323 | MR | Zbl

[16] R. Sacksteder Foliations and pseudogroups, American journal of Mathematics, Volume 87 (1967), pp. 79-101 | MR | Zbl

[17] É. Salem Une généralisation du théorème de Myers-Steenrod aux pseudogroupes d'isométries locales, Annales de l'institut Fourier, Volume 38 (1988) no. 2, pp. 185-200 | Numdam | MR | Zbl

[18] R. Schoen On the conformal and CR automorphism groups, Geometric and functional analysis, Volume 5 (1995) no. 2, pp. 464-481 | MR | Zbl

[19] D. Trotsenko Continuation from a domain and the approximation of space quasiconformal mappings with small distortion coefficient, Soviet mathematics, Doklady, Volume 27 (1983) no. 3, pp. 777-780 | Zbl

[20] J. Väisälä Lectures on n-dimensional quasiconformal mappings, Lecture Notes in Mathematics, Springer-Verlag, 1988 | MR

[21] I. Vaisman Conformal foliations, Kodai Math. Journal, Volume 2 (1979), pp. 26-37 | MR | Zbl

[22] R.A. Wolak Foliated G-structures and Riemannian foliations, Manuscripta Mathematica, Volume 66 (1989), pp. 45-59 | MR | Zbl

Cité par Sources :