This is an introductory graduate course on Riemannian manifolds. We shall cover Chapters 09 of do Carmo, Riemannian Geometry, with some omissions and some supplementary material (e.g., Cartan structure equations).
Instructor: 

TA: 
Chenyun Luo 
Time: 
TuTh 10:3011:45 
Classroom: 
Maryland 202 
Text: 
M. P. do Carmo,
Riemannian Geometry, 1992 
Supplementary references: 
J.
Lee, Riemannian Geometry, 1997 S.
Gallot, D. Hulin, J.
Lafontaine, Riemannian Geometry,
3rd ed., 2004 
Prerequisite: 
Undergraduate
analysis and linear algebra. Some knowledge of topology is recommended. 
Grading: 
There
will be weekly problem sets and no exams. 
Syllabus: 
The
syllabus will be updated as the semester progresses. Be sure to check this
page before starting work on any assignment. 
week 
beginning 
reading 
assignment
(due the following Tuesday) 
1 
Thu. Sep. 1 
Ch. 0, Sec. 12 
(no assignment) 
2 
Sep. 6 
Ch. 0, Sec. 35 
Ch. 0: 1, 2, 5, 9ac, 12ab 
3 
Sep. 13 
Ch. 1 
Ch. 0: 7, 11. Ch. 1: 2, 3, 4, 6 
4 
Sep. 20 
Ch. 2, Lee,
pp. 1121 
Ch. 2: 1, 2, 3 
5 
Sep. 27 
Ch. 3, Sec. 12 
Ch. 1: 7. Ch. 2: 4,
7, 8 Ch. 3: 1, 2 
6 
Oct. 4 
Ch. 3, Sec. 34 
Gallot: 1.118a. Ch. 3: 3a, 4, 5 
7 
Oct. 11 
Ch. 4, Sec. 13 
Ch. 4: 4, 5, 7 
8 
Oct. 18 
Ch. 4, Sec. 45 
No
class Oct. 20 (Fall Break) 

Oct. 25 
no class this week 
Ch. 3: 7. Ch. 4: 8, 10 
9 
Nov. 1 
Ch. 5 
Ch. 5: 1, 3, 6, 7 
10 
Nov. 8 

(no assignment) 
11 
Nov. 15 
Ch. 6, Sec. 12 
Ch. 6: 3, 5, 6, 7 

Nov. 22 
Thanksgiving
break 

12 
Nov. 29 
Ch. 7 
Ch.
7: 5, 6, 9, 10, 12 
13 
Dec. 6 
Ch. 8: Sec. 3 
Gallot: 2.11ac. Ch. 9: 1, 3 (due
Dec. 14) 
14 
Mon, Dec. 12 
Ch. 9 
Class
meetings: Dec. 12 &14, 1:002:15 (Gilman 217) 
Last updated
12/8/2016