Abstract
A flag on a manifold M is an increasing sequence of foliations ℱ 1 ,⋯,ℱ p on this manifold, where for each i, dimℱ i =i. The aim of this paper is to etablish that any flag of riemannian foliations 𝒟= ℱ 1 ,⋯,ℱ p on a compact and connected manifold, lifts on the bundle of transverse direct orthonormal frames of ℱ p to a flag of transversally parallelizable foliations. This result permits us to obtain a classification of riemannian flags of a n+1-dimensional compact manifold for which the dimension of the structural Lie algebra of the flow is equal to n or n-1.
Highlights
On appelle drapeau de feuilletages sur une variété M de dimension n, une suite D = (F1, · · ·, Fp) de feuilletages de Fi où dim Fi = i; ce drapeau est dit complet si p = n − 1.Ici, nous cherchons à généraliser le résultat de P
The aim of this paper is to etablish that any flag of riemannian foliations D =
us to obtain a classification of riemannian flags
Summary
On appelle drapeau de feuilletages sur une variété M de dimension n, une suite D = (F1, · · · , Fp) de feuilletages de Fi où dim Fi = i; ce drapeau est dit complet si p = n − 1. Nous cherchons à généraliser le résultat de P. Molino [7] sur le relèvement d’un feuilletage riemannien en un feuilletage transversalement parallélisable. On obtient que tout drapeau de feuilletages riemanniens se relève sur une certaine variété compacte en un drapeau de feuilletages transversalement parallélisables (théorème de relèvement)
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