Contents:Chapter 1. Manifolds
1.1 Review of calculus
1.2 Manifolds:definitions and examples
1.3 Vectors and differentials
1.4 Submanifolds
1.5 Riemann metrics
Chapter 2. Tensor Calculus
2.1 Tensors:definitions
2.2 Differential forms
2.3 Differential calculus
2.4 Integral calculus
2.5 Lie derivatives
Chapter 3. Connections and curvature
3.1 Connections
3.2 Geodesics
3.3 Riemann curvature
3.4 Gauss curvature
3.5 Cartan’s mobile frame
3.6 Levi-Civita’s connection
3.7 Curvature identities
Chapter 4. Special topics
4.1 General Relativity
4.2 Schwarzschild metric
4.3 The group SO(3)
4.4 Weyl’s gauge theory paper of 1929. |