The Geometry of Lagrange Spaces: Theory and Applications: 59 - Rilegato

Miron, R.; Anastasiei, Mihai

Rilegato

ISBN 10: 0792325915 ISBN 13: 9780792325918

Casa editrice: Springer-Verlag GmbH, 1993

Riassunto

Differential-geometric methods are gaining increasing importance in the understanding of a wide range of fundamental natural phenomena. Very often, the starting point for such studies is a variational problem formulated for a convenient Lagrangian. From a formal point of view, a Lagrangian is a smooth real function defined on the total space of the tangent bundle to a manifold satisfying some regularity conditions. The main purpose of this book is to present: (a) an extensive discussion of the geometry of the total space of a vector bundle; (b) a detailed exposition of Lagrange geometry; and (c) a description of the most important applications. New methods are described for construction geometrical models for applications.
The various chapters consider topics such as fibre and vector bundles, the Einstein equations, generalized Einstein--Yang--Mills equations, the geometry of the total space of a tangent bundle, Finsler and Lagrange spaces, relativistic geometrical optics, and the geometry of time-dependent Lagrangians. Prerequisites for using the book are a good foundation in general manifold theory and a general background in geometrical models in physics.
For mathematical physicists and applied mathematicians interested in the theory and applications of differential-geometric methods.

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Contenuti

I. Fibre Bundles, General Theory. II. Connections in Fibre Bundles. III. Geometry of the Total Space of a Vector Bundle. IV. Geometrical Theory of Embeddings of Vector Bundles. V. Einstein Equations. VI. Generalized Einstein--Yang--Mills Equations. VII. Geometry of the Total Space of a Tangent Bundle. VIII. Finsler Spaces. IX. Lagrange Spaces. X. Generalized Lagrange Space. XI. Applications of the GLn Spaces with the Metric Tensor e2sigma(x,y)gammaij(x,y). XII. Relativistic Geometrical Optics. XIII. Geometry of Time Dependent Lagrangians. Bibliography. Index.

Product Description

Book by Miron R Anastasiei Mihai

Dettagli dell'edizione

• Editore: Springer-Verlag GmbH
• Data di pubblicazione: 1993
• Lingua: Inglese
• ISBN 10: 0792325915
• ISBN 13: 9780792325918
• Rilegatura: Copertina rigida
• Numero di pagine: 304
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Germania