AWM-MAA Etta Z. Falconer Lecture 1999

Lecturer: Chuu-Lian Terng, Northeastern University

Title: Geometry and Visualization of Surfaces

Abstract: One of the high points of 19th century mathematics was the study of the geometry of surfaces in ℝ³. The first fundamental form of a surface is the metric induced by the inner product of ℝ³, and the second fundamental form is the quadratic form associated with the differential of the unit normal field. They satisfy the Gauss and Codazzi equations which lead to interesting.partial differential equations when natural geometric conditions are imposed on the surface. Many classes of surfaces (e.g., surfaces with constant mean curvature, surfaces with constant Gaussian curvature, and isothermic surfaces) lead to soliton equations. In this talk, I’ll explain basic concepts and properties in surface theory and use Richard Palais’ 3D-filmstrip computer visualization program to display some of these remarkable surfaces.