Exponential Map and Curvature Tensor

This lecture covers the exponential map, Riemann normal coordinates, covariant derivatives, connection coefficients, parallel transport, Levi-Civita connection, geodesics, and the Riemann curvature tensor. It explains how the covariant derivatives do not commute in the presence of curvature and introduces Riemann normal coordinates to define a coordinate system in the neighborhood of a point.