An Introduction to Manifolds

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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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Tu, Loring W. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer New York : Imprint: Springer, 2011.
Edición:2nd ed. 2011.
Colección:Universitext,
Temas:
Manifolds (Mathematics).
Global analysis (Mathematics).
Geometry, Differential.
Manifolds and Cell Complexes.
Global Analysis and Analysis on Manifolds.
Differential Geometry.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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