Differential Geometry

1 Course Unit

The course moves from a study of extrinsic geometry (curves and surfaces in n-space) to the intrinsic geometry of manifolds. After a review of vector calculus and a section on tensor algebra, we study manifolds and their intrinsic geometry, including metrics, connections, geodesics, and the Riemann curvature tensor. Topics include Eulerian curvature and Euler's theorems, the Gauss map and first/second fundamental forms, the Theorema Egregium, minimal surfaces in n-space; other topics as time permits. Not Offered Every Year Mutually Exclusive: MATH 4650 Prerequisite: (MATH 2400 OR MATH 2600) AND (MATH 3140 OR MATH 5140) 1 Course Unit