Differential Geometry.

Catalog description

This course examines the local and global geometric and topological properties of curves and surfaces in 3-dimensional Euclidean space. Topics will include curvature and torsion of space curves, mean and Guassian curvature of surfaces, and the Gauss-Bonnet theorem. In addition, the course will also examine smooth Riemannian manifolds, the curvature tensor, geodesics, and applications such as surfaces of constant mean curvature.