Feuilleter
no. 3
Turbulent holomorphic foliations on compact complex tori and transversely holomorphic Cartan geometry
[Feuilletages holomorphes tourbillonnés sur les tores complexes compacts et géométrie de Cartan transverse]
Indranil Biswas1 ; Sorin Dumitrescu2
1Department of Mathematics, Shiv Nadar University, NH91, Tehsil Dadri, Greater Noida, Uttar Pradesh 201314, India
2Université Côte d’Azur, CNRS, LJAD, France
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 35 (2026) no. 3, pp. 785-800

We define a class of nonsingular holomorphic foliations on compact complex tori which generalizes (in higher codimension) the turbulent foliations of codimension one constructed by Ghys in [12]. For those smooth turbulent foliations we prove that all transversely holomorphic Cartan geometries are flat. We also establish a uniqueness result for the transversely holomorphic Cartan geometries.

Nous introduisons une classe de feuilletages holomorphes non singuliers sur les tores complexes compacts qui généralise (en codimension arbitraire) les feuilletages holomorphes turbulents de codimension un construits par Ghys dans [12]. Nous démontrons que toute géométrie de Cartan holomorphe transverse à un tel feuilletage holomorphe turbulent est nécessairement plate. Nous prouvons également un résultat d’unicité pour la géométrie de Cartan transverse.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/afst.1863
Classification : 32S65, 53C10, 53C30
Keywords: holomorphic foliation, compact complex torus, transversely complex projective structure, Cartan geometry, transversely Cartan geometry
Mots-clés : feuilletage holomorphe, tore complexe compact, structure projective transverse, géométrie de Cartan, géométrie de Cartan transverse

Indranil Biswas  1   ; Sorin Dumitrescu  2

1 Department of Mathematics, Shiv Nadar University, NH91, Tehsil Dadri, Greater Noida, Uttar Pradesh 201314, India
2 Université Côte d’Azur, CNRS, LJAD, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Indranil Biswas; Sorin Dumitrescu. Turbulent holomorphic foliations on compact complex tori and transversely holomorphic Cartan geometry. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 35 (2026) no. 3, pp. 785-800. doi: 10.5802/afst.1863
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     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
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