Titlebook: Metric Foliations and Curvature; Detlef Gromoll,Gerard Walschap Book 2009 Birkhäuser Basel 2009 Riemannian manifold.curvature.differential

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Book 2009mannian manifolds, particularly those with positive or nonnegative sectional curvature. In fact, all known such spaces are constructed from only a representative handful by means of metric fibrations or deformations thereof...This text is an attempt to document some of these constructions, many of w

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Book 2009hich have only appeared in journal form. The emphasis here is less on the fibration itself and more on how to use it to either construct or understand a metric with curvature of fixed sign on a given space..

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Metric Foliations in Space Forms, are concerned. Surprisingly, a complete classification of metric foliations on spaces of constant curvature is not yet available. There does, however, exist a classification of metric ., at least in nonnegative curvature, which will be described in this chapter.

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https://doi.org/10.1007/978-3-7643-8715-0Riemannian manifold; curvature; differential geometry; foliation; manifold; space form

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Birkhäuser Basel 2009

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Metric Foliations and Curvature978-3-7643-8715-0Series ISSN 0743-1643 Series E-ISSN 2296-505X

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Submersions, Foliations, and Metrics,omorphisms. 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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Open Manifolds of Nonnegative Curvature,6], who gave a thorough account of their topology. Apart from some special cases, however, their metric structure has only been understood fairly recently. It illustrates the key role that Riemannian submersions seem to play in nonnegative curvature.

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