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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.

Course Coordinator
Fatma Özdemir
Fatma Özdemir
Course Language
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