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.
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© 2009 Birkhäuser Verlag AG
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(2009). Submersions, Foliations, and Metrics. In: Metric Foliations and Curvature. Progress in Mathematics, vol 268. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8715-0_1
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DOI: https://doi.org/10.1007/978-3-7643-8715-0_1
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8714-3
Online ISBN: 978-3-7643-8715-0
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