Lie groupoids and semi-local models of Singular Riemannian foliations

Abstract

We describe a local model for any Singular Riemannian Foliation in a neighbourhood of a closed saturated submanifold of a regular stratum. Moreover we construct a Lie groupoid which controls the transverse geometry of the linear approximation of the Singular Riemannian Foliation around these submanifolds. We also discuss the closure of this Lie groupoid and its Lie algebroid.

We have completely rewritten the introduction,and added new results such asTheorem 1.6 , (about closure of Lie subgroupoids) , Propositions 6.5 and 6.7.(about the Lie algebroid structure of the Lie groupoid that describe the dynamical behavior of Singular Riemannian foliations)