Buy metric foliations and curvature progress in mathematics on amazoncom free shipping on qualified orders. This text is an attempt to document some of these constructions many of which 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. Get this from a library metric foliations and curvature detlef gromoll gerard walschap riemannian manifolds particularly those with positive or nonnegative curvature are constructed from only a handful by means of metric fibrations or deformations thereof this text documents some of . In the past three or four decades there has been increasing realization that metric foliations play a key role in understanding the structure of riemannian manifolds particularly those with positive or nonnegative sectional curvature in fact all known such spaces are constructed from only a. One therefore expects those riemannian manifolds with the largest amount of symmetry namely space forms to be the ones that display the most variety as far as these foliations are concerned surprisingly a complete classification of metric foliations on spaces of constant curvature is not yet available
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