21-360 Differential Geometry of Curves and Surfaces

9 units, Carnegie Mellon University

The course is a rigorous introduction to the differential and integral calculus of curves and surfaces. Topics to be covered include Parameterized and regular curves Frenet equations canonical coordinate system, local canonical forms, global properties of plane curves Regular surfaces, differential functions on surfaces, the tangent plane and differential of a map, orientation of surfaces, characterization of compact orientable surfaces, classification of compact surfaces The geometry of the Gauss map, isometries and conformal maps, parallel transport, geodesics, the GaussBonnet theorem and applications. More topics may be covered, as time allows. Students should be prepared to write proofs and perform computations. 21356 or 21236 are recommended. Three 50 minute lectures

Prerequisites: 21-269 or 21-268

Offered: Spring 2027

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