SUR LES FEUILLETAGES TRANSVERSALEMENT HOMOGÈNES A SOUS-GROUPE DISCRET.

Hassimiou Diallo (1)

1 LMF - Laboratoire de Mathématiques Fondamentales

G{Γ} being the group generated by left translation of a Lie group G and right translation of elements of a discrete subgroup Γ, we establish here that on a manifold M, there is a correspondance one to one between (G/Γ)- homogenous transversally foliations and foliations given by a (G{Γ} ,G)- transverse structure, and two corresponding foliations have the same C^{∞}-transverse structure. Moreover one foliation of (G{Γ} ,G)- transverse structure is a Lie foliation if and only if its Γ-holonomy group is trivial.

Mots clés: extension de feuilletage; feuilletage de Lie; feuilletage transversalement homogène; (G; extension de feuilletage.; T)-structure transverse

Domaines: Géométrie différentielle [math.DG]

Hassimiou Diallo. SUR LES FEUILLETAGES TRANSVERSALEMENT HOMOGÈNES A SOUS-GROUPE DISCRET.. Rendiconti di Matematica e delle sue Applicazioni, 2015, Série VII (36), pp.197-206. ⟨hal-01066566v2⟩