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Feuilletages holomorphes admettant une mesure transverse invariante
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 24 (2015) no. 3, pp. 523-541.

Soit un feuilletage holomorphe régulier de codimension 1 sur une variété kählerienne compacte. On suppose que admet un courant positif invariant par holonomie. Le but de cette note est d’établir l’alternative suivante :

  • – Il existe une hypersurface invariante par le feuilletage.
  • – Le feuilletage admet une métrique hermitienne transverse de courbure constante invariante par holonomie.

Let be a regular codimension 1 holomorphic foliation on a compact Kähler manifold. One assumes in addition that possesses a transverse invariant positive current. The aim of this paper is to establish the following alternative:

  • – There exists an invariant hypersurface.
  • – The foliation admits a transverse invariant hermitian metric with constant curvature.
Reçu le :
Accepté le :
Publié le :
DOI : https://doi.org/10.5802/afst.1454
Classification : 37F75
Mots clés : Holomorphic foliations, invariant current, invariant metric
@article{AFST_2015_6_24_3_523_0,
     author = {Fr\'ed\'eric Touzet},
     title = {Feuilletages holomorphes admettant une mesure transverse invariante},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {523--541},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {6e s{\'e}rie, 24},
     number = {3},
     year = {2015},
     doi = {10.5802/afst.1454},
     mrnumber = {3403731},
     language = {fr},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1454/}
}
Frédéric Touzet. Feuilletages holomorphes admettant une mesure transverse invariante. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 24 (2015) no. 3, pp. 523-541. doi : 10.5802/afst.1454. https://afst.centre-mersenne.org/articles/10.5802/afst.1454/

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