Geodesic Curves: Minimizing Distance and Constant Speed

This lecture discusses geodesic curves parameterized at constant speed to minimize the distance between two points. The instructor explains the concept of geodesic curves and their properties, such as minimizing distances and being parameterized at constant speed. The lecture covers the theorem related to geodesic curves and their behavior when minimizing distances. It also delves into the concept of geodesic rest and the conditions under which a curve is considered geodesic. The lecture concludes with a discussion on the normal curvature of regular curves and their geodesic properties.