Extension d'un feuilletage de Lie minimal d'une vari\'{e}t\'{e} compacte

TL;DR

This paper proves that extensions of minimal Lie foliations on compact manifolds are transversally Riemannian with trivial normal bundle, enabling classification via Lie subgroups.

Contribution

It establishes a classification framework for extensions of minimal Lie foliations on compact manifolds using Lie subgroup structures.

Findings

Extensions are transversally Riemannian with trivial normal bundle

Classification of extensions via Lie subgroups

Provides a structural understanding of minimal Lie foliation extensions

Abstract

The purpose of this paper is to show that any extension of a minimal Lie foliation on a compact manifold is a transversaly Riemannian g\h- foliation with trivial normal bundle. This result permits to classify the extensions of a minimal Lie foliation on a compact manifold from the Lie subgroups of its Lie group.