Pfaffian Systems, K-Symplectic Systems - Rilegato

Awane, Azzouz; Goze, Michel

Rilegato

ISBN 10: 0792363736 ISBN 13: 9780792363736

Casa editrice: Kluwer Academic Pub, 2000

Riassunto

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.

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Contenuti

Introduction. 1. Exterior Forms. 2. Exterior Systems. 3. k-Symplectic Exterior Systems. 4. Pfaffian Systems. 5. Classification of Pfaffian Systems. 6. k-Symplectic Manifolds. 7. k-Symplectic Affine Manifolds. 8. Homogeneous k-Symplectic G-Spaces. 9. Geometric Pre-Quantization.

Dettagli dell?edizione

• Editore: Kluwer Academic Pub
• Data di pubblicazione: 2000
• ISBN 10: 0792363736
• ISBN 13: 9780792363736
• Rilegatura: Copertina rigida
• Lingua: Inglese
• Numero di pagine: 240
• Contatto del produttore: {language_tag:it_IT,value:"Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com"}