On the connection between isometric immersions and covering projections
Résumé
In this paper we give some necessary and sufficient conditions under which an isometric immersion between two connected Riemannian manifolds of the same dimension becomes a covering projection. We also prove that, generally, even if these conditions are not satisfied, we can always associate to such an isometric immersion i:X→Y a family of covering projections. They are constructed by removing a suitable closed set from X and then restricting i to the connected components of the remaining manifolds. Some applications are given to the problem of the classification of a class of complete metrics with singularities on an analytic manifold.