MATH 372 Differential Geometry

General concepts of geometry. Coordinates in Euclidean space. Riemannian metric. Pseudo-Euclidean space and Lobachevsky geometry. Flat curves. Space curves. The theory of surfaces in three-dimensional space. The concept of area. Curvature. The second fundamental form. Gaussian curvature. Invariants of a pair of quadratic forms. Euler’s theorem. Complex analysis and geometry. Conformal transformations. Isotermal coordinates. The concept of a manifold. Geodesics.