Differential Geometry: Surfaces

This lecture covers the differential geometry of parametric surfaces, including topics such as tangent space, metric, normal curvature, principal curvatures, mean curvature, and Gaussian curvature. It explains how curves on a surface are defined, tangent vectors of curves, and the computation of normal curvature. The lecture also delves into the concept of principal curvatures, surface curvatures, asymptotic directions, and asymptotic curves.