Math 217A--Differential Geometry--Winter 2013

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

Class Days

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), Friday (3/15)



Required Text

"Riemannian Geometry" by Manfredo do Carmo

The Toponogov theorem will be taken from a set of notes which is here.

Announcements

Homework

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.