Pfaffian Systems, k-Symplectic Systems by A. AwanePfaffian Systems, k-Symplectic Systems by A. Awane

Pfaffian Systems, k-Symplectic Systems

byA. Awane, M. Goze

Paperback | December 12, 2011

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The geometrical view of mechanics is based on the study of certain exterior systems, the most classical of which are Pfaffian systems. In this book, we present the classification theorems (Frobenius, Darboux) and the local classification of Pfaffian systems of five variables, following Cartan. We also present a new class of exterior systems, called k-symplectic systems, generalizing the notion of symplectic form. These systems permit us to write in the language of exterior forms the equations proposed by Nambu for a model of statistical mechanics. Audience: This book is aimed at graduate students and at research workers in the field of mathematics, differential geometry, statistical mechanics, mathematics of physics and Lie algebras.
Title:Pfaffian Systems, k-Symplectic SystemsFormat:PaperbackDimensions:253 pages, 9.25 × 6.1 × 0.03 inPublished:December 12, 2011Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048154863

ISBN - 13:9789048154869

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Table of Contents

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.