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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
- Idioma
- Publicado en
- 2017
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- Título
- Differential Geometry
- Subtítulo
- Connections, Curvature, and Characteristic Classes
- Idioma
- Inglés
- Autores
- Loring W. Tu
- Editorial
- Springer
- Publicado en
- 2017
- Formato
- Tapa dura
- Páginas
- 368
- ISBN13
- 9783319550824
- Serie
- Etiquetas
- No ficción, Ciencia y Matemáticas, Matemáticas, Geometría
- Calificación
- 4 de 5
- Descripción
- 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.