MATH 443:Differential Geometry

Arclength, curvature and torsion of a curve. Geometry of surfaces. Curvature, first and second fundamental form, Christofel symbols. Geodesics. Parallel vector fields. Surfaces of constant Gaussian curvature. Introduction to manifolds, tangent spaces and tangent bundles. Vector fields and Lie brackets. Parallel vector fields on manifolds and Riemannian manifolds.