Advertisement

Metric Foliations and Curvature

  • Detlef Gromoll
  • Gerard Walschap

Part of the Progress in Mathematics book series (PM, volume 268)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Back Matter
    Pages 165-176

About this book

Introduction

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.

Keywords

Riemannian manifold curvature differential geometry foliation manifold space form

Authors and affiliations

  • Detlef Gromoll
    • 1
  • Gerard Walschap
    • 2
  1. 1.State University of New YorkStony BrookUSA
  2. 2.Department of MathematicsUniversity of OklahomaNormanUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-7643-8715-0
  • Copyright Information Birkhäuser Basel 2009
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-7643-8714-3
  • Online ISBN 978-3-7643-8715-0
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site