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Services
Commerciaux
14, rue de Provigny
94236 CACHAN
CEDEX
FRANCE
Tél.: +33 (0)1 47 40
67 00
Fax: +33 (0)1 47 40
67 02
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le livre de AWANE
The geometrical view of mechanics is based on the study of certain exterior systems, the most classical of which are Pfaffian systems. This book presents the classification theorems (Frobenius, Darboux) and the local classification of Pfaffian systems of five variables, following Cartan. It also presents a new class of exterior systems, called k-symplectic systems, generalizing the notion of symplectic form. It is aimed at graduate students and at research workers in the field of mathematics, differential geometry, statistical mechanics, mathematics of physics and Lie algebras.
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.