Math 660

Here is the official course syllabus. This includes information on topics we plan to cover, the homework, midterm, and class presentation.

A list of exercises (to do on your own) and problems (to write up carefully and turn in) will be posted here after each class meeting.

Lecture 1: review of smooth manifolds (due Thurs 9/15)

Lecture 2: Riemannian metrics (due Thurs 9/22)

Lecture 3: Connections (due Thurs 9/22)

Lecture 4-5: Geodesics (due Thurs 9/29)

Lecture 6-7: Curvature (due Thurs 10/6)

Lecture 8-9: Jacobi fields (due Thurs 10/20)

Lecture 10-11: Riemannian submanifolds (due Thurs 10/27)

Lecture 12-13: Gauss--Bonnet and complete manifolds (midterm due Thurs 11/3)

Lecture 14--15: Hadamard's theorem, constant curvature spaces (due Thurs 11/10)

Lecture 16--20: Bonnet--Myers, Morse Index Theorem, etc. (due Thurs 12/1)