MAT 417E - Theory of Surfaces

Course Objectives

1. To provide students with basic knowledges on regular surface and the concepts of differential geometry of surfaces in 3-dimensional Euclidean space;
2. To introduce Gauss egregium theorem and the structure equations of surfaces such as Gauss equations, Mainardi-Codazzi equations.
3. To introduce geodesics of surfaces, the Gauss-Bonnet theorem and exponential map.

Course Description

Surfaces in 3-dimensional Euclidean space. First Fundamental Form. Mappings of surfaces. Geometry of the Gauss map. Ruled Surfaces. Minimal surfaces. Intrinsic properties. Theorema Egregium of Gauss. Geodesics. Gauss-Bonnet Theorem. Exponential map.