Richard Schoen, 383T, 725-0854, schoen "at" math
Office hours: Tu 4:00-5:00, F 3:30-4:30 or by appointment
This course will cover connections and curvature, but will place emphasis on Riemannian geometry. Topics will include the Levi-Civita connection, Riemann curvature tensor, Ricci and scalar curvature, geodesics, parallel transport, completeness, geodesics and Jacobi fields, comparison techniques including the Toponogov comparison theorem and some of its consequences.
There will be four homework assignments given throughout the quarter which will be posted on this webpage. There will be no inclass examinations.
Classroom and time: Building 200, Room 305, Time: 2:15-3:30
Week one: Friday (1/11)
Week two: Monday (1/14), Wednesday (1/16), Friday (1/18)
Week three: No class this week
Week four: Monday (1/28), Wednesday (1/30), Friday (2/1)
Week five: Wednesday (2/6), Friday (2/8)
Week six: Wednesday (2/13), Friday (2/15)
Week seven: Wednesday (2/20), Friday (2/22)
Week eight: Wednesday (2/27), Friday (3/1)
Week nine: Monday (3/4)
Week ten: Monday (3/11), Wednesday (3/13)
"Riemannian Geometry" by Manfredo do Carmo
The Toponogov theorem will be taken from a set of notes which is here.
Here is the first homework assignment. The homework is due Monday, January 28 at classtime.
Here is the second homework assignment. The homework is due Friday, February 8 at classtime.
Here is the third homework assignment. The homework is due Friday, February 22 at classtime.
Here is the fourth homework assignment. The homework is due Monday, March 11 at classtime.