MAT 342E - Differantial Geometry

Course Objectives

1. To give the student essentials of curves and surfaces in Euclid spaces,
2. To reinforce their advanced calculus and linear algebra knowledge and to give an ability to apply this knowledge on geometry problems

Course Description

Differential geometry of curves; osculating plane, curvature and torsion, Frenet curves in the Euclid space E^n and Frenet formulae, Curves in S^2 nd S^3, Curves with constant Frenet curvatures. Natural equations, the fundamental theorem of theory of curves. Natural equations, the fundamental theorem of the theory of curves. Differential geometry of surfaces; first and second fundamental forms of a surface, normal curvature, the lines of curvature, asymptotic curves, Dupin indicatrix, Meunier’s theorem, mean curvature, Gaussian curvature. Gauss’s Theorema Egregium.