Submersions, Foliations, and Metrics
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.
KeywordsRiemannian Manifold Sectional Curvature Holonomy Group Riemannian Submersion Riemannian Foliation
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