Lecture 6
Topics
- Curvature
- Parallel transport of a tensor around a closed curve
- The Riemann tensor \(R^\rho{}_{\sigma\mu\nu} \)
- \([\nabla_\mu,\nabla_\nu] \) acting on tensor fields
- Symmetries of the Riemann tensor, Bianchi identities
- Contractions of the Riemann tensor: Ricci tensor, Ricci scalar, Einstein tensor, Weyl tensor
- Geodesic deviation equation
Bibliography
Practicing
- Problems
- Slides:computation of the change \(\delta V^\mu \) of a vector when it is parallel transported along an infinitesimal closed curve.
Videos
Related video lectures by the instructor. There is partial overlap with the course curriculum, use at your own discretion! Check the video lectures page for details...
