Nicht aus der Schweiz? Besuchen Sie lehmanns.de
Introduction to Global Variational Geometry -  Demeter Krupka

Introduction to Global Variational Geometry (eBook)

eBook Download: PDF
2000 | 1. Auflage
500 Seiten
Elsevier Science (Verlag)
978-0-08-095426-4 (ISBN)
Systemvoraussetzungen
218,16 inkl. MwSt
(CHF 209,95)
Der eBook-Verkauf erfolgt durch die Lehmanns Media GmbH (Berlin) zum Preis in Euro inkl. MwSt.
  • Download sofort lieferbar
  • Zahlungsarten anzeigen
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
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

Front Cover 1
Dimension Theory 4
Copyright Page 5
Contents 10
Preface 6
Chapter 1. Dimension Theory of Separable Metric Spaces 12
1.1. Definition of the small inductive dimension 14
1.2. The separation and enlargement theorems for dimension 0 21
1.3. The sum, Cartesian product, universal space, compactification and embedding theorems for dimension 0 31
1.4. Various kinds of disconnectedness 42
1.5. The sum, decomposition, addition, enlargement, separation and Cartesian product theorems 52
1.6. Definitions of the large inductive dimension and the covering dimension. Metric dimension 62
1.7. The compactification and coincidence theorems. Characterization of dimension in terms of partitions 71
1.8. Dimensional properties of Euclidean spaces and the Hilbert cube. Infinite-dimensional spaces 82
1.9. Characterization of dimension in terms of mappings to spheres. Cantor-manifolds. Cohomological dimension 98
1.10. Characterization of dimension in terms of mappings to polyhedra 110
1.11. The embedding and universal space theorems 129
1.12. Dimension and mappings 144
1.13. Dimension and inverse sequences of polyhedra. 154
1.14. Dimension and axioms 165
Chapter 2. The Large Inductive Dimension 172
2.1. Hereditarily normal and strongly hereditarily normal spaces 173
2.2. Basic properties of the dimension Ind in normal and hereditarily normal spaces 181
2.3. Basic properties of the dimension Ind in strongly hereditarily normal spaces 193
2.4. Relations between the dimensions ind and Ind . Cartesian product theorems for the dimension Ind 208
Chapter 3. The Covering Dimension 218
3.1. Basic properties of the dimension dim in normal spaces. Relations between the dimensions ind, Ind and dim 219
3.2. Characterizations of the dimension dim in normal spaces. Cartesian product theorems for the dimension dim 237
3.3. The compactification and the universal space theorems for the dimension dim. The dimension dim and inverse systems of compact spaces 252
Chapter 4. Dimension Theory of Metrizable Spaces 262
4.1. Basic properties of dimension in metrizable spaces 263
4.2. Characterizations of dimension in metrizable spaces. The universal space theorem 278
4.3. Dimension and mappings in metrizable spaces 288
Bibliography 300
List of special symbols 318
Author index 320
Subject index 323

PDFPDF (Adobe DRM)

Kopierschutz: Adobe-DRM
Adobe-DRM ist ein Kopierschutz, der das eBook vor Mißbrauch schützen soll. Dabei wird das eBook bereits beim Download auf Ihre persönliche Adobe-ID autorisiert. Lesen können Sie das eBook dann nur auf den Geräten, welche ebenfalls auf Ihre Adobe-ID registriert sind.
Details zum Adobe-DRM

Dateiformat: PDF (Portable Document Format)
Mit einem festen Seiten­layout eignet sich die PDF besonders für Fach­bücher mit Spalten, Tabellen und Abbild­ungen. Eine PDF kann auf fast allen Geräten ange­zeigt werden, ist aber für kleine Displays (Smart­phone, eReader) nur einge­schränkt geeignet.

Systemvoraussetzungen:
PC/Mac: Mit einem PC oder Mac können Sie dieses eBook lesen. Sie benötigen eine Adobe-ID und die Software Adobe Digital Editions (kostenlos). Von der Benutzung der OverDrive Media Console raten wir Ihnen ab. Erfahrungsgemäß treten hier gehäuft Probleme mit dem Adobe DRM auf.
eReader: Dieses eBook kann mit (fast) allen eBook-Readern gelesen werden. Mit dem amazon-Kindle ist es aber nicht kompatibel.
Smartphone/Tablet: Egal ob Apple oder Android, dieses eBook können Sie lesen. Sie benötigen eine Adobe-ID sowie eine kostenlose App.
Geräteliste und zusätzliche Hinweise

Buying eBooks from abroad
For tax law reasons we can sell eBooks just within Germany and Switzerland. Regrettably we cannot fulfill eBook-orders from other countries.

Mehr entdecken
aus dem Bereich