Symmetries and Conservation Laws

This lecture covers Killing vectors, conserved quantities, maximally symmetric spaces, and the properties of the Riemann curvature tensor. It explains geodesics, the Riemann tensor in the presence of curvature, and the Ricci tensor. The instructor discusses the Einstein equations, the Weyl tensor, and the Einstein tensor. The lecture also delves into the symmetries of the Riemann tensor, Killing vector fields, and the conservation of energy-momentum tensor. Examples and proofs related to these concepts are provided.