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 these constructions, many of which have only appeared in
journal form. The emphasis 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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