Class meetings: MWF 10:00-10:50 MATH 0104
Text: Riemannian Geometry by Manfredo do Carmo
Grading and Homework: to be discussed at the first class meeting.
 

Riemannian geometry is both an active area of research in its own right and an indispensable prerequisite to research in such other disciplines as  algebraic geometry and relativity theory.  MATH 740 is an introduction to Riemannian geometry, and every effort will be made to keep it relatively self-contained.

Here is a link to the lecture notes for the first three lectures, as  contributed by Benjamin Howard, Sean Lawton, and Chris Fleming, and edited by me. The lecture notes will be updated as I receive further contributions.

Here are lectures 4-6,  courtesy of Elisha Peterson, Tina Horvath, Dave Saranchak and Pete Rankel.

Here are lectures 7-9, originally taken by Ben, Sean and Chris

Here are lectures 10-13 (I think). They include a considerably improved treatment of the covariant derivative and curvature for the hyperbolic plane.

Here is another installment. I have lost track of the lecture numbers, but this brings us through the material on Jacobi fields, of which I think, considerably improved the treatment.

Here are the lectures between October 18 and October 27.

Here are the notes on complex manifolds.