Pfaffian Systems, k-Symplectic Systems

  • Azzouz Awane
  • Michel Goze

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Azzouz Awane, Michel Goze
    Pages 1-21
  3. Azzouz Awane, Michel Goze
    Pages 23-34
  4. Azzouz Awane, Michel Goze
    Pages 35-65
  5. Azzouz Awane, Michel Goze
    Pages 67-97
  6. Azzouz Awane, Michel Goze
    Pages 99-142
  7. Azzouz Awane, Michel Goze
    Pages 143-172
  8. Azzouz Awane, Michel Goze
    Pages 173-190
  9. Azzouz Awane, Michel Goze
    Pages 191-215
  10. Azzouz Awane, Michel Goze
    Pages 217-232
  11. Back Matter
    Pages 233-240

About this book

Introduction

The theory of foliations and contact forms have experienced such great de­ velopment recently that it is natural they have implications in the field of mechanics. They form part of the framework of what Jean Dieudonne calls "Elie Cartan's great theory ofthe Pfaffian systems", and which even nowa­ days is still far from being exhausted. The major reference work is. without any doubt that of Elie Cartan on Pfaffian systems with five variables. In it one discovers there the bases of an algebraic classification of these systems, their methods of reduction, and the highlighting ofthe first fundamental in­ variants. This work opens to us, even today, a colossal field of investigation and the mystery of a ternary form containing the differential invariants of the systems with five variables always deligthts anyone who wishes to find out about them. One of the goals of this memorandum is to present this work of Cartan - which was treated even more analytically by Goursat in its lectures on Pfaffian systems - in order to expound the classifications currently known. The theory offoliations and contact forms appear in the study ofcompletely integrable Pfaffian systems of rank one. In each of these situations there is a local model described either by Frobenius' theorem, or by Darboux' theorem. It is this type of theorem which it would be desirable to have for a non-integrable Pfaffian system which may also be of rank greater than one.

Keywords

Grad algebra differential geometry field lie algebra manifold

Authors and affiliations

  • Azzouz Awane
    • 1
  • Michel Goze
    • 2
  1. 1.Faculté des SciencesUniversité Hassan IICasablancaMaroc
  2. 2.Faculté des Sciences et TechniquesUniversité de Haute AlsaceMulhouseFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-9526-1
  • Copyright Information Springer Science+Business Media B.V. 2000
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5486-9
  • Online ISBN 978-94-015-9526-1
  • About this book
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