Manifolds, Vector Fields, and Differential Forms An Introduction to Differential Geometry

This textbook serves as an introduction to modern differential geometry at a level accessible to advanced undergraduate and master's students. It places special emphasis on motivation and understanding, while developing a solid intuition for the more abstract concepts. In contrast to graduate l...

Full description

Bibliographic Details
Main Authors: Gross, Gal, Meinrenken, Eckhard (Author)
Format: eBook
Language:English
Published: Cham Springer International Publishing 2023, 2023
Edition:1st ed. 2023
Series:Springer Undergraduate Mathematics Series
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • 1. Introduction
  • 2. Manifolds
  • 3. Smooth maps
  • 4. Submanifolds
  • 5. Tangent spaces
  • 6. Vector fields
  • 7. Differential forms
  • 8. Integration
  • 9. Vector bundles
  • Notions from set theory
  • Notions from algebra
  • Topological properties of manifolds
  • Hints and answers to in-text questions
  • References
  • List of Symbols
  • Index