The Geometry of Lagrange Spaces: Theory and Applications
By: by Radu Miron, Mihai Anastasiei
Contributors: Anastasiei, Mihai
Series: Fundamental Theories of Physics, An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application -- 59; Fundamental Theories of Physics, An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application -- 59
Publisher: Springer Netherlands
Published: 1994
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] /
Number of pages: 289
ISBN-13: 9789401043380; 9789401107884
Subjects: Global differential geometry; Mathematics; Physics
Description: 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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