COURSE DESCRIPTION
Introduction to differential geometry, centered on notions of curvature. Starts with curves in the plane, and proceeds to higher dimensional submanifolds. Computations in coordinate charts: first and second fundamental form, Christoffel symbols. Discusses the distinction between extrinsic and intrinsic aspects, in particular Gauss' theorema egregium. The Gauss-Bonnet theorem. Geodesics. Examples such as hyperbolic space.
Prerequisites: 18.100, 18.06, 18.700, 18.701
Text Book: Differential Geometry of Curves and Surfaces / Manfredo P. DoCarmo
Working Groups:
- Group 1: Ganesh, Shi, Norman. - Responsible for the 1st and 7th problems
- Group 2: Daniel, Pagonakis, Casey. - Responsible for the 2nd and 8th problems
- Group 3: Felipe, Peter B., Hunter. - Responsible for the 3rd and 9th problems
- Group 4: Yutao, Panagiotis, Brian. - Responsible for the 4th and 10th problems
- Group 5: Mark, Guanna Qu, Victor. - Responsible for the 5th and 11th problems
- Group 6: Weishuang, Anchen, Sadovnik. - Responsible for the 6th and 12th problems
