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The Geometry of Lagrange Spaces: Theory and Applications

  • Radu Miron
  • Mihai Anastasiei

Part of the Fundamental Theories of Physics book series (FTPH, volume 59)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Radu Miron, Mihai Anastasiei
    Pages 1-18
  3. Radu Miron, Mihai Anastasiei
    Pages 19-34
  4. Radu Miron, Mihai Anastasiei
    Pages 35-65
  5. Radu Miron, Mihai Anastasiei
    Pages 66-79
  6. Radu Miron, Mihai Anastasiei
    Pages 80-93
  7. Radu Miron, Mihai Anastasiei
    Pages 94-105
  8. Radu Miron, Mihai Anastasiei
    Pages 106-128
  9. Radu Miron, Mihai Anastasiei
    Pages 129-156
  10. Radu Miron, Mihai Anastasiei
    Pages 157-179
  11. Radu Miron, Mihai Anastasiei
    Pages 180-202
  12. Radu Miron, Mihai Anastasiei
    Pages 223-249
  13. Radu Miron, Mihai Anastasiei
    Pages 250-275
  14. Back Matter
    Pages 276-289

About this book

Introduction

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.

Keywords

Einstein equations Mathematica Tensor covariant derivative curvature dynamics electromagnetic field electromagnetic fields fibre bundles gauge transformation geometry magnetic field manifold model transformation

Authors and affiliations

  • Radu Miron
    • 1
  • Mihai Anastasiei
    • 1
  1. 1.Faculty of MathematicsUniversity “Al. I. Cuza”IaşiRomania

Bibliographic information

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