MA 562: Introduction to Differential Geometry and Topology
2:30- 3:20 PM, M/W/F, REC 313

Instructor Office Office hour Email
Dr. Chi Li MATH 734 Tuesday 9:30am-11:00am and Thursday 1:30-3:00pm or by appointment li2285@purdue.edu


Textbook William M. Boothby: An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised, Volume 120, Second Edition (Pure and Applied Mathematics) (2)

Reference M.P. Do Carmo: Differential Geometry of Curves and Surfaces

Lecture Notes (updating)

Homework Homework should be submitted every two weeks in Friday class (before the class). For example, HW1 is due on 9/8 and so on.
Grading:
Homework Midterms Final Total
25 25 50 100
Syllabus (updating)

Week

Sections

References

Homework (lecture notes)

Week 1: 8/21-8/25

Geometry of surfaces

[Boothby, VIII.1]
[DoCarmo, 2-2 to 2-5]

1,2,3,4,5,6

Solution by T.W.Liu

Solution by E.Ng

Week 2: 8/28-9/1

Gauss curvature, mean curvature

[Boothby, VIII.2]
[DoCarmo, 3-2 to 3-3]

Week 3: 9/4-9/8

Gauss's Theorem Egregium [Boothby, VIII.2]
[DoCarmo, 4-3]
7,8,9,10,11

Solution by C. Meng et al.

Solution by E.Ng

Week 4: 9/11-9/15

Gauss-Bonnet formula

[DoCarmo, 4-5]

Week 5: 9/18-9/22

Differentiable manifolds

Examples

[Boothby, III.1-2]

12, 13, 14, 15, 16, 17, 18 (due on Oct 6)

HW 3 Solution by C. Meng et al.

Week 6: 9/25-9/29

Submanifolds

Differentiable mapping, Immersions

[Boothby, III.3-5]

Week 7: 10/2-10/6

Lie groups

[Boothby, III.6-8]

19-25 (due on Oct 20)

Week 8: 10/9-10/13

Tangent and cotangent spaces [Boothby, IV.1-2] 10/9-10/10: October Break

homework: 26-33 (due Nov 3)

Week 9: 10/16-10/20

Vector fields, Lie bracket

One paramter groups

Week 10: 10/23-10/27

Frobenius theorem

Week 11: 10/30-11/3

Differential forms

De Rham cohomology groups

Week 12: 11/6-11/10

Integration on manifolds

Stokes' Theorem on manifolds

Week 13: 11/13-11/17

Riemannian metrics

Week 14: 11/20-11/24

Geodesics

11/22-11/25: Thanksgiving Vacation

Week 15: 11/27-12/1

Geodesics

Curvatures of Riemannian metrics

Week 16: 12/4-12/8

Curvatures of Riemannian metrics