GR3 · Curvature
A 18-module path through gr3 · curvature, in study order from foundations to the frontier.
Modules
- Riemann Curvature Tensor
- Curvature as the Commutator of Covariant Derivatives
- Geometric Meaning of Curvature via Parallel Transport
- Algebraic Symmetries of the Riemann Tensor
- Independent Components of the Riemann Tensor
- First (Algebraic) Bianchi Identity
- Second (Differential) Bianchi Identity
- Ricci Tensor
- Ricci Scalar
- Einstein Tensor
- Contracted Bianchi Identities
- Weyl Conformal Tensor
- Ricci Decomposition of the Riemann Tensor
- Sectional Curvature
- Geodesic Deviation and the Tidal Tensor
- Curvature Invariants and Scalar Polynomials
- Curvature in Two and Three Dimensions
- Curvature 2-Form and Cartan's Structure Equations