An Introduction to Manifolds

• Κύριος συγγραφέας: Tu, Loring W. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York, 2011.
• Σειρά: Universitext,
• Θέματα: Mathematics.; Global analysis (Mathematics).; Manifolds (Mathematics).; Differential geometry.; Complex manifolds.; Manifolds and Cell Complexes (incl. Diff.Topology).; Global Analysis and Analysis on Manifolds.; Differential Geometry.

Manifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined i...

Πίνακας περιεχομένων:

• Preface to the Second Edition
• Preface to the First Edition
• Chapter 1. Euclidean Spaces
• Chapter 2. Manifolds
• Chapter 3. The Tangent Space
• Chapter 4. Lie Groups and Lie Algebras.-Chapter 5. Differential Forms
• Chapter 6. Integration.-Chapter 7. De Rham Theory
• Appendices
• A. Point-Set Topology
• B. The Inverse Function Theorem on R(N) and Related Results
• C. Existence of a Partition of Unity in General
• D. Linear Algebra
• E. Quaternions and the Symplectic Group
• Solutions to Selected Exercises
• Hints and Solutions to Selected End-of-Section Problems
• List of Symbols
• References
• Index.