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, or 18.701
Text Book: Differential geometry of curves and surfaces / Manfredo P. do Carmo.
Differential geometry : curves - surfaces - manifolds / Wolfgang Kuhnel ; translated by Bruce Hunt.
RECENT UPDATES
[09.14.2010] HW assignments due Thursdays at 3pm in 2-108 see problem sets
