Pfaffian Systems, k-Symplectic Systems
By: by Azzouz Awane, Michel Goze
Contributors: Goze, Michel
Publisher: Springer Netherlands
Published: 2000
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] /
Number of pages: 240
ISBN-13: 9789048154869; 9789401595261
Subjects: Global differential geometry; Mathematics; Algebra
Description: 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.
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