Curves and Surfaces

Description

This course concerns the geometry of smooth curves and surfaces in R 3 . The main property we will study is curvature, first for curves, and then the more complex concept of the curvature of a surface. We’ll see various definitions and understand how they are related, and learn how (unlike for curves) the curvature of a surface is an intrinsic property, which can be defined without referring to the ambient R 3 . We’ll also begin to see how local curvature is related to the global shape of the surface.