Introduction to Global Variational Geometry: Volume 71
Published in June 2008
Book
Hardback
500 pages
978-0-444-53046-2 (ISBN)
Description
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
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
More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Elsevier Science & Technology
Target group
Professional and scholarly
Dimensions
Height: 225 mm
Width: 150 mm
ISBN-13
978-0-444-53046-2 (9780444530462)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
Content
Tentative Table of Contents:
Preface
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
Appendices
Bibliography
Index
Preface
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
Appendices
Bibliography
Index