MATH 635 - DIFFERENTIAL GEOMETRY - WINTER 2014

Time and Place: 11-12 pm MWF in EH 1060
Instructor: Ralf Spatzier, 5850 East Hall, 763-2192, spatzier@umich.edu
Office Hours: Monday and Wednesday 12 -1 and by appointment. Besides individual office hours, there will also be a group office hour, Tuesdays 5-6 in EH 4088.
Prerequisites Introductory material from topology, algebraic topology and manifolds on the level of our alpha courses
Course Outline: This course is an introduction to differential geometry. We will discuss the basic ideas of connections, Riemannian metrics, curvature and the basic tools in the subject, especially variational methods, Jacobi fields, and comparison theorems. After those more local ideas, we will turn to global differential geometry which relates geometric ideas to the underlying topology. Examples are sphere theorems, structural results both in positive and negative curvature, and rigidity theorems. If time permits we will pursue more advanced topics.
Homework: I will assign homework on a weekly basis. You will hand in written solutions. In addition, you can present and discuss solutions orally during a group office hour. If you do not present at these office hours, you are expected to present the solutions to me orally during individual office hours.
Quizzes and Final: There will be several oral quizzes during the term. The final will be a mix of written and oral final.
Grading Policy: homework 40%; quizzes 30%, final exam 30%;
Book: Do Carmo, Riemannian Geometry, Birkhauser. The book is optional but highly recommended.
Homeworks : Homework 1            Homework 2            Homework 3            Homework 4            Homework 5