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2. Differential Geometry

Differential geometry is the study of manifolds, along with the respective behaviour of coordinates and functions on manifolds. In this section, we will explore the foundations of differential geometry, Cartan theory, and later formalisms used in the study of gravitation.

• 2.1. Manifolds
• 2.2. Vectors and tensors
• 2.3. Forms
• 2.4. Component expansions

References:

• Göckeler M. and Schücker T. Differential geometry, gauge theories, and gravity. Cambridge Univ. Press, 1999.

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1.2. Vector spaces

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2.1. Manifolds