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Focusing on the historical evolution of connection and curvature, this graduate-level introduction to differential geometry caters to mathematics and physics students. It explores significant milestones such as Gauss' Theorema Egregium and the Gauss-Bonnet theorem while elucidating the Chern-Weil theory of characteristic classes on principal bundles. The book includes exercises to reinforce understanding and illustrates theoretical extensions. A foundational knowledge of manifolds and differential forms is essential, with de Rham cohomology required for the latter sections.
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Differential Geometry, Loring W. Tu
- Language
- Released
- 2017
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- (Hardcover)
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- Subtitle
- Connections, Curvature, and Characteristic Classes
- Language
- English
- Authors
- Loring W. Tu
- Publisher
- Springer
- Released
- 2017
- Format
- Hardcover
- Pages
- 368
- ISBN13
- 9783319550824
- Series
- Rating
- 4 out of 5
- Description
- Focusing on the historical evolution of connection and curvature, this graduate-level introduction to differential geometry caters to mathematics and physics students. It explores significant milestones such as Gauss' Theorema Egregium and the Gauss-Bonnet theorem while elucidating the Chern-Weil theory of characteristic classes on principal bundles. The book includes exercises to reinforce understanding and illustrates theoretical extensions. A foundational knowledge of manifolds and differential forms is essential, with de Rham cohomology required for the latter sections.