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Pfaffian Systems, k-Symplectic Systems

  • Book
  • © 2000

Overview

Authors:
  1. Azzouz Awane

    1. Faculté des Sciences, Université Hassan II, Casablanca, Maroc

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  2. Michel Goze

    1. Faculté des Sciences et Techniques, Université de Haute Alsace, Mulhouse, France

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    You can also search for this author in PubMed   Google Scholar

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Exterior Forms

    • Azzouz Awane, Michel Goze
    Pages 1-21

  3. Exterior Systems

    • Azzouz Awane, Michel Goze
    Pages 23-34

  4. k-Symplectic Exterior Systems

    • Azzouz Awane, Michel Goze
    Pages 35-65

  5. Pfaffian Systems

    • Azzouz Awane, Michel Goze
    Pages 67-97

  6. Classification of Pfaffian Systems

    • Azzouz Awane, Michel Goze
    Pages 99-142

  7. k-Symplectic Manifolds

    • Azzouz Awane, Michel Goze
    Pages 143-172

  8. k-Symplectic Affine Manifolds

    • Azzouz Awane, Michel Goze
    Pages 173-190

  9. Homogeneous k-Symplectic G-Spaces

    • Azzouz Awane, Michel Goze
    Pages 191-215

  10. Geometric Pre-Quantization

    • Azzouz Awane, Michel Goze
    Pages 217-232

  11. Back Matter

    Pages 233-240
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Keywords

About this book

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.

Authors and Affiliations

  • Faculté des Sciences, Université Hassan II, Casablanca, Maroc

    Azzouz Awane

  • Faculté des Sciences et Techniques, Université de Haute Alsace, Mulhouse, France

    Michel Goze

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