110.645 Riemannian Geometry   --  Fall 2016

This is an introductory graduate course on Riemannian manifolds. We shall cover Chapters 0-9 of do Carmo, Riemannian Geometry, with some omissions and some supplementary material (e.g., Cartan structure equations).

Instructor:

Bernard Shiffman

TA:

Chenyun Luo

Time:

TuTh 10:30-11:45

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. 1-2

(no assignment)

2

Sep. 6

Ch. 0, Sec. 3-5

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. 11-21

Ch. 2: 1, 2, 3

5

Sep. 27

Gallot, pp. 41-46

Ch. 3, Sec. 1-2

Ch. 1: 7.  Ch. 2: 4, 7, 8

Ch. 3: 1, 2

6

Oct. 4

Ch. 3, Sec. 3-4

Gallot: 1.118a.  Ch. 3: 3a, 4, 5

7

Oct. 11

Ch. 4, Sec. 1-3

Ch. 4: 4, 5, 7

8

Oct. 18

Ch. 4, Sec. 4-5

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. 1-2

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

Gallot, pp. 34, 56-57

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, 1:00-2:15 (Gilman 217)


Last updated 12/8/2016