na aula 8.
Singular Riemannian foliations generalize isometric group actions and encode rich transverse geometry. In the polar case, the leaf space carries a natural orbifold structure.
We introduce and study a class of singular Riemannian foliations with sections that we call Coxeter polar foliations. We obtain two main reconstruction results. First, we prove that, for a singular Riemannian foliation admitting sections, every Riemannian orbifold metric on the leaf space is induced by a Riemannian metric on the ambient manifold adapted to the foliation. Second, we show that the leaf space of a Coxeter polar foliation admits a complete system of weights that uniquely determines both the foliation and the ambient manifold up to foliated diffeomorphism.
This is part of an ongoing collaboration with Diego Corro.