1999 AWM-MAA Invited Lecture
Geometry and Visualization of Surfaces
Monday, August 2, 1999
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.
Biographical Information: Professor Chuu-Lian Terng received her B.S. from National Taiwan University and her Ph.D. from Brandeis University. She is currently a professor at Northeastern University. Before joining Northeastern, she spent two years at the University of California, Berkeley and four years at Princeton University. She also spent two years at the Institute for Advanced Study (IAS) in Princeton and two years at the Max-Planck Institute in Bonn Germany.
Her early research concerned the classification of natural vector bundles and natural differential operators between them. She then became interested in submanifold geometry. Her main contributions are developing a structure theory for isoparametric submanifolds in Rn and constructing soliton equations from special submanifolds. Recently, Terng and Karen Uhlenbeck (University of Texas at Austin) have developed a general approach to integrable PDEs that explains their hidden symmetries in terms of loop group actions. She is co-author of the book Submanifold Geometry and Critical Point Theory and an editor of the Journal of Differential Geometry survey volume 4 on "Integrable systems".
Professor Terng served as President of the Association for Women in Mathematics (AWM) from 1995 to 1997 and as Member-at-Large of the Council of the American Mathematical Society (AMS) from 1989 to 1992. She is currently on the Advisory Board of the National Center for Theoretical Sciences in Taiwan, the Steering Committee of the IAS/Park City Summer Institute, and the Editorial Board of the Transactions of the AMS. She received a Sloan Fellowship in 1980 and a Humboldt Senior Scientist Award in 1997.