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Birkhäuser

Metric Foliations and Curvature

  • Book
  • © 2009

Overview

Authors:
  1. Detlef Gromoll

    1. State University of New York, Stony Brook, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Gerard Walschap

    1. Department of Mathematics, University of Oklahoma, Norman, USA

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    You can also search for this author in PubMed   Google Scholar

  • 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)

  1. Front Matter

    Pages i-viii
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  2. Submersions, Foliations, and Metrics

    Pages 1-44

  3. Basic Constructions and Examples

    Pages 45-108

  4. Open Manifolds of Nonnegative Curvature

    Pages 109-134

  5. Metric Foliations in Space Forms

    Pages 135-164

  6. Back Matter

    Pages 165-176
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Keywords

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.

Reviews

From the reviews: “The book under review is one of five or six books on foliations that should be in the professional library of every geometer. … authors define the fundamental tensors of a Riemannian submersion tensors that carry over to a metric foliation on M … . gives a brief introduction to the geometry of the second tangent bundle and related topics needed for the study of metric foliations on compact space forms of non negative sectional curvature … .” (Richard H. Escobales, Jr., Mathematical Reviews, Issue 2010 h)

Authors and Affiliations

  • State University of New York, Stony Brook, USA

    Detlef Gromoll

  • 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: 978-3-7643-8714-3Published: 19 February 2009

  • eBook ISBN: 978-3-7643-8715-0Published: 28 March 2009

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: VIII, 176

  • Topics: Differential Geometry

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