Coming soon
This note is part of the planned structure of the general relativity sequence and has not been written yet.
This section page is a stable landing point; the sub-topics below will be filled in over time.
Sequence
- 01. Affine Connections and Covariant Derivatives
- 02. Parallel Transport and Geodesics
- 03. The Levi-Civita Connection; Metric Compatibility
- 04. The Riemann Tensor; Bianchi Identities
- 05. Ricci, Scalar, Weyl; the Einstein Tensor
- 06. Geodesic Deviation and the Jacobi Equation
- 07. Killing Vectors and Isometries
- 08. Tetrads (Frame Fields) and the Cartan Structure Equations
- 09. The Petrov Classification
- 10. Hypersurfaces; Induced Metric and Extrinsic Curvature (Gauss-Codazzi)
- 11. Comparison Geometry and the Morse Index Theorem
- 12. Holonomy and the Berger Classification