Riemannian Geometry Lecturer: Prof. Roger Bielawski Assistant: Joseph Malkoun Main textbook for the course: Riemannian Geometry, by S. Gallot, D. Hulin and J. Lafontaine. Homework 1 is now available: Homework 1 Solution to Homework 1 Homework 2 is now available (due Friday November 2, 2012): Homework 2 Solution to Homework 2 Homework 3 is now available (due Friday November 9, 2012): Homework 3 Solution to Homework 3 Homework 4 is now available (due Friday November 16, 2012): Homework 4 Solution to Homework 4 Homework 5 is now available (due Friday November 23, 2012): Homework 5 Solution to Homework 5 Homework 6 is now available (due Friday November 30, 2012): Homework 6 Solution to Homework 6 Homework 7 is now available (due Friday December 7, 2012): Homework 7 Solution to Homework 7 Homework 8 is now available (due Friday December 21, 2012): Homework 8 Solution to Homework 8 Homework 9 is now available (due Friday January 11, 2013): Homework 9 Solution to Homework 9 Homework 10 is now available (due Friday January 18, 2013): Homework 10 Solution to Homework 10 Homework 11 is now available (due Friday January 25, 2013): Homework 11 Solution to Homework 11 Homework 12 is now available (but you don't have to hand it in!): Homework 12 Stereographic projection of the n-sphere minus the North pole N onto the equatorial plane. It can be used to define the standard smooth structure on the n-sphere with just two patches. You can also find a very short proof that the hyperbolic plane has constant negative curvature and is geodesically complete here: a few simple facts about the hyperbolic plane. Who was Bernhard Riemann? Wikipedia article