Introduction to Global Variational Geometry

Demeter Krupka

• Publisher: Elsevier Science
• Year: 2000
• Print ISBN: 9780720405019
• eBook ISBN: 9780080954240
• Topic: Mathematics
• Subtopic: Geometry
• Index: Mathematics

This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether's theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles- First book on the geometric foundations of Lagrange structures- New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity- Basic structures and tools: global analysis, smooth manifolds, fibred spaces

Table of contents

• Front Cover
• Some Classes of Singular Equations
• Copyright Page
• CONTENTS
• Introduction
• Chapter 1. Noether Operators
• Chapter 2. Abstract Singular Equations of Normal Type
• Chapter 3. Special Singular Equations of Normal Type
• Chapter 4. Abstract Singular Equations of Non-Normal Type
• Chapter 5. Wiener-Hopf Integral Equations of Non-Normal Type and their Discrete Analogue
• Chapter 6. Singular Integral Equations of Non -Normal Type
• Chapter 7. Systems of Singular Equations of Normal Type
• Chapter 8. Systems of Singular Equations of Non-Normal Type
• Chapter 9. Singular Equations in some Countably Normed Spaces and Spaces of Distributions
• Chapter 10. Singular Equations with Discontinuous Functions
• Chapter 11. Approximation Methods for the Solution of Singular Equations
• Bibliography
• Symbol index
• Author index
• Subject index