Monographs in Mathematics

Geometry of Foliations

Authors: Tondeur, Philippe

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About this book

The topics in this survey volume concern research done on the differential geom­ etry of foliations over the last few years. After a discussion of the basic concepts in the theory of foliations in the first four chapters, the subject is narrowed down to Riemannian foliations on closed manifolds beginning with Chapter 5. Following the discussion of the special case of flows in Chapter 6, Chapters 7 and 8 are de­ voted to Hodge theory for the transversal Laplacian and applications of the heat equation method to Riemannian foliations. Chapter 9 on Lie foliations is a prepa­ ration for the statement of Molino's Structure Theorem for Riemannian foliations in Chapter 10. Some aspects of the spectral theory for Riemannian foliations are discussed in Chapter 11. Connes' point of view of foliations as examples of non­ commutative spaces is briefly described in Chapter 12. Chapter 13 applies ideas of Riemannian foliation theory to an infinite-dimensional context. Aside from the list of references on Riemannian foliations (items on this list are referred to in the text by [ ]), we have included several appendices as follows. Appendix A is a list of books and surveys on particular aspects of foliations. Appendix B is a list of proceedings of conferences and symposia devoted partially or entirely to foliations. Appendix C is a bibliography on foliations, which attempts to be a reasonably complete list of papers and preprints on the subject of foliations up to 1995, and contains approximately 2500 titles.

Table of contents (13 chapters)

  • Examples and Definition of Foliations

    Tondeur, Philippe

    Pages 1-5

  • Foliations of Codimension One

    Tondeur, Philippe

    Pages 7-16

  • Holonomy, Second Fundamental Form, Mean Curvature

    Tondeur, Philippe

    Pages 17-31

  • Basic Forms, Spectral Sequence, Characteristic Form

    Tondeur, Philippe

    Pages 33-42

  • Transversal Riemannian Geometry

    Tondeur, Philippe

    Pages 43-68

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-3-0348-8914-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-3-7643-5741-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-3-0348-9825-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometry of Foliations
Authors
Series Title
Monographs in Mathematics
Series Volume
90
Copyright
1997
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8914-8
DOI
10.1007/978-3-0348-8914-8
Hardcover ISBN
978-3-7643-5741-2
Softcover ISBN
978-3-0348-9825-6
Series ISSN
1017-0480
Edition Number
1
Number of Pages
VIII, 310
Topics