Mean and Gaussian Curvature

This lecture covers the concepts of mean curvature and Gaussian curvature, focusing on the average of curvatures in all directions and the principal curvatures. It explains how to calculate the mean curvature for each orthonormal basis of the tangent plane, providing detailed proofs and examples. Additionally, it discusses the relationship between the mean curvature and the Gaussian curvature, emphasizing the importance of understanding the curvature properties of surfaces. The lecture concludes with a corollary on the mean curvature for a given surface, highlighting the significance of these curvature measures in differential geometry.