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Pfaffian Systems, K-Symplectic Systems - Azzouz Awane

Pfaffian Systems, K-Symplectic Systems

Hardcover Published: 30th June 2000
ISBN: 9780792363736
Number Of Pages: 240

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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.

Introduction
Exterior Forms
Exterior Systems
k-Symplectic Exterior Systems
Pfaffian Systems
Classification of Pfaffian Systems
k-Symplectic Manifolds
k-Symplectic Affine Manifolds
Homogeneous k-Symplectic G-Spaces
Geometric Pre-Quantization
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780792363736
ISBN-10: 0792363736
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 240
Published: 30th June 2000
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 1.6
Weight (kg): 0.54

Earn 339 Qantas Points
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