Math 240 Riemannian Geometry, Fall 2018

Instructor: Song Sun

Office: 839 Evans Hall

Office Hours: Monday 2-3, Thursday 10.00-11.00, or by appointment

References

Required Text:

John Lee. "Riemannian Manifolds: An Introduction to Curvature"

Recommended Texts:

John Milnor. "Morse Theory".
Do Carmo. "Riemannian Geometry".
S. Gallot, D. Hulin and J. Lafontaine. "Riemannian Geometry".
Marcel Berger. "A Panoramic View of Riemannian Geometry".

Prerequisite

Math 214, or equivalent. You need to have a good understanding of basic notions on differentiable manifolds.

Syllabus

This is a course aiming to introduce the foundational concepts in Riemannian geometry. The first half of the semester will cover most material in Lee's book, but we will not follow exactly the order in the book. The second half will be an introduction to selected more advanced topics.

We will have bi-weekly homework assignments, which will be posted in time on this webpage. [L] refers to Lee's book.

Homework 1 (Due 9/20 in class). [L]: Problem 3-7 (P45), 4-3(P63), 4-5(P64), Exercise 4.12 (P62).
Homework 2 (Due 10/4 in class). [L]: Problem 6-1, 6-3, 6-4, 6-5 (P112-113).
Homework 3 (Due 10/18 in class). [L]: Problem 3-8 (P45), 5-9(P89), 7-2(P128), Exercise 10.1(P176)
Homework 4 (Due 11/1 in class). [L]: Problem 5-5 (P88), 8-3, 8-4, 8-11 (P150-152).
Homework 5 (Due 11/15 in class). [L]: Problem 3-4, 3-5, 3-9 (P44-P46), 8-12 (P152).
Homework 6 (Due 11/29 in class). [L]: Problem 7-4 (P128), Problem 8-6, 8-7, 8-8 (P151).