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- Studies the main tool that is used for creating spaces of positive or nonnegative curvature
- As yet, there is no comprehensive survey of this topic
- Includes supplementary material: sn.pub/extras
Part of the book series: Progress in Mathematics (PM, volume 268)
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Table of contents (4 chapters)
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Front Matter
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Back Matter
About this book
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 representative handful by means of metric fibrations or deformations thereof.
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.
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Authors and Affiliations
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State University of New York, Stony Brook, USA
Detlef Gromoll
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Department of Mathematics, University of Oklahoma, Norman, USA
Gerard Walschap
Bibliographic Information
Book Title: Metric Foliations and Curvature
Authors: Detlef Gromoll, Gerard Walschap
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-3-7643-8715-0
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Basel 2009
Hardcover ISBN: 978-3-7643-8714-3
eBook ISBN: 978-3-7643-8715-0
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: VIII, 176
Topics: Differential Geometry