What is differential geometry: curves and surfaces

22 Dec 2020 · Anton Petrunin, Sergio Zamora Barrera ·

These notes are designed for those who either plan to work in differential geometry, or at least want to have a good reason not to do it. We discuss smooth curves and surfaces -- the main gate to differential geometry. We focus on the techniques that are absolutely essential for further study, keeping it problem-centered, elementary, visual, and virtually rigorous.