## 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...