Course:Differentiable Manifolds II, Math 519, Section M1
Time: TR 9:30--10:50am.
Location: 149 Henry Administration Bldg
Instructor: Chris Leininger
Phone: 265-6763
Email: clein (at) math.uiuc.edu
Office: 265 Altgeld Hall
Office hours: TBA
Text(s):
The books will be put on reserve in the library. We will primarily cover chapter 1--9 from Do Carmo's book, but will supplement from the other three books as needed.

Homework: I will make 5 to 7 assignments throughout the course of the semester. These will not be collected, but to get the most from the class, I strongly suggest doing these assignments. I will have problem sessions periodically (scheduled throughout the semester) in which we can discuss problems from any of the problem sets.

Grading: Grades are based entirely on class participation.

Syllabus: Riemannian geometry: Riemannian metrics, connections, geodesics, parallel transport, curvature. Some generalizations of these notions to other bundles. Theorems of Hopf--Rinow, Bonnet--Myers, Hadamard, Cartan; Comparison Geometry; Flat Torus Theorem; Spaces of constant curvature and space forms.

Homework:
Lectures:
Class notes: I will be gone a few times throughout the semester. The problem sessions will be considered as the make-up classes for these.

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