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Geometry of Foliations

  • Philippe Tondeur

Part of the Monographs in Mathematics book series (MMA, volume 90)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Philippe Tondeur
    Pages 1-5
  3. Philippe Tondeur
    Pages 7-16
  4. Philippe Tondeur
    Pages 43-68
  5. Philippe Tondeur
    Pages 69-79
  6. Philippe Tondeur
    Pages 81-97
  7. Philippe Tondeur
    Pages 99-106
  8. Philippe Tondeur
    Pages 107-112
  9. Philippe Tondeur
    Pages 113-115
  10. Philippe Tondeur
    Pages 117-127
  11. Philippe Tondeur
    Pages 129-131
  12. Philippe Tondeur
    Pages 133-137
  13. Back Matter
    Pages 139-305

About this book

Introduction

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.

Keywords

Finite Mean curvature Riemannian geometry curvature differential geometry equation geometry

Authors and affiliations

  • Philippe Tondeur
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Bibliographic information