Gaussian Curvature and Geodesics

This lecture covers the determination of the derivative of the length of curves on a surface, the deformation of curves with fixed ends, and the concept of geodesics. It also delves into the typology of points on a surface, such as elliptical, hyperbolic, and parabolic points, and the intrinsic properties of surfaces. The lecture concludes with the parametrization of spheres and the classification of surfaces based on their isometric properties.