Submersions, Foliations, and Metrics

Abstract

The concept of submersion is dual to what is arguably the oldest notion in differential geometry, that of immersion. Both are generalizations of diffeomorphisms. In the presence of a Riemannian metric, it is natural to consider distance-preserving maps rather than diffeomorphisms. These in turn generalize to isometric immersions, and their metric dual, Riemannian submersions.