Differential Geometry: Lecture 17: on principal,aymptotic and geodesic curves

Here we describe principal, asymptotic and geodesic curves on a surface in R3. Several lemmas from O'neill are proved and we conclude with a brief discussion of the surface of revolution (5.7) as a special application of the formulas in Lecture 16. Next up, the study of surfaces via Cartan's exterior calculus.