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Riemannian Foliations

  • Pierre Molino

Part of the Progress in Mathematics book series (PM, volume 73)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Pierre Molino
    Pages 1-31
  3. Pierre Molino
    Pages 33-67
  4. Pierre Molino
    Pages 69-101
  5. Pierre Molino
    Pages 103-145
  6. Pierre Molino
    Pages 147-183
  7. Pierre Molino
    Pages 185-216
  8. Back Matter
    Pages 217-343

About this book

Introduction

Foliation theory has its origins in the global analysis of solutions of ordinary differential equations: on an n-dimensional manifold M, an [autonomous] differential equation is defined by a vector field X ; if this vector field has no singularities, then its trajectories form a par­ tition of M into curves, i.e. a foliation of codimension n - 1. More generally, a foliation F of codimension q on M corresponds to a partition of M into immersed submanifolds [the leaves] of dimension ,--------,- - . - -- p = n - q. The first global image that comes to mind is 1--------;- - - - - - that of a stack of "plaques". 1---------;- - - - - - Viewed laterally [transver­ 1--------1- - - -- sally], the leaves of such a 1--------1 - - - - -. stacking are the points of a 1--------1--- ----. quotient manifold W of di­ L..... -' _ mension q. -----~) W M Actually, this image corresponds to an elementary type of folia­ tion, that one says is "simple". For an arbitrary foliation, it is only l- u L ally [on a "simpIe" open set U] that the foliation appears as a stack of plaques and admits a local quotient manifold. Globally, a leaf L may - - return and cut a simple open set U in several plaques, sometimes even an infinite number of plaques.

Keywords

Division Finite Isometrie Partition Riemannian geometry Vector field differential equation equation field foliation form global analysis manifold ordinary differential equation set

Authors and affiliations

  • Pierre Molino
    • 1
  1. 1.Institut de MathématiquesUniversité des Sciences et Techniques du LanguedocMontpellier CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-8670-4
  • Copyright Information Birkhäuser Boston 1988
  • Publisher Name Birkhäuser Boston
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-8672-8
  • Online ISBN 978-1-4684-8670-4
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
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