Sur une classe de groupoides riemanniens

TL;DR

This paper demonstrates the existence of a Riemannian groupoid associated with the closures of leaves in a regular Riemannian foliation on a compact manifold, linking it to a transformational groupoid.

Contribution

It establishes a connection between Riemannian groupoids and the closures of leaves in Riemannian foliations, extending the understanding of their structure and equivalence.

Findings

Existence of a Riemannian groupoid for leaf closures

Equivalence with a transformational groupoid on the basic manifold

Extension of Haefliger's generalized sense of equivalence

Abstract

In this work we show that there is a Riemannian groupoid whose orbits are the closures of the leaves of a regular Riemannian foliation on a compact manifold. This groupoid is equivalent (in a generalized sense of Haefliger) with a transformational groupoid on the basic manifold.