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Introduction to Global Variational Geometry - Demeter Krupka

Introduction to Global Variational Geometry


Published: 1st April 2000
Format: PDF
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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

Tentative Table of Contents:
List of Standard Symbols
Chapter 1: Smooth Manifolds
Chapter 2: Analysis on Manifolds
Chapter 3: Lie Transformation Groups
Chapter 4: Lagrange Structures
Chapter 5: Elementary Sheaf Theory
Chapter 6: Variational Sequences on Fibered Manifolds
Chapter 7: Invariant Variational Functionals on Principal Bundles
Chapter 8: Differential Invariants
Chapter 9: Natural Variational Principles

ISBN: 9780080954295
ISBN-10: 0080954294
Format: PDF
Language: English
Number Of Pages: 196
Published: 1st April 2000
Publisher: Elsevier Science