ANNEAU DE FEUILLETAGES D'’UNE VARIETE p-RIEMANNIENNE.

Hassimiou Diallo (1)

1 LMF - Laboratoire de Mathématiques Fondamentales

Locally, a almost pproduct manifold is a polytope of a product of p varieties model , with changes card that are products of p morphisms . We show that a almost p-product manifold is characterized by the data of a complete and stable family of p non trivial foliations; and then this family generates a Boolean ring over which the subset consisting of Lie foliations is a "fi…nal section" for Boolean algebra associated (that’s to say, in this ring, any extension of a Lie foliation is a Lie foliation). In addition, we establish that when the family foliations are Riemannian foliations , every foliations of this ring are both metric and parallel. Finally, in remaining still in this context, we give under certain conditions, cohomological obstructions to the existence of a structure almost product.

Mots clés: drapeau de feuilletages; feuilletage riemannien; feuilletage de Lie; feuilletage parallèle; extension de feuilletage; drapeau de feuilletages.

Domaines: Géométrie différentielle [math.DG]

Hassimiou Diallo. ANNEAU DE FEUILLETAGES D'’UNE VARIETE p-RIEMANNIENNE.. 2014. ⟨hal-01066563v1⟩