Geodesics and Parallel Transport

This lecture covers exercises related to geodesics, parallel transport, and the Riemann tensor on two-dimensional manifolds. Starting with the geodesic equation and its simplification, the exercises progress to finding explicit solutions, considering specific cases, and exploring the commutator of covariant derivatives. The lecture also delves into the Riemann tensor, scalar curvature, and constant curvature conditions. Additionally, it discusses the equivalence principle and the deviation of geodesics in curved space, emphasizing the role of the Riemann tensor in determining distances. The exercises provide a comprehensive understanding of these fundamental concepts in differential geometry.