MATH4030 - Differential Geometry - 2019/20

Course Name: 
Course Year: 


  • There is no tutorial in the first week.
  • Lecture notes from previous years are available under "Useful Links". Also, a brief notes for preliminary materials is posted.
  • Class schedule changes: we will have a double lecture on Oct 17 and a double tutorial on Oct 24.
  • The midterm will take place on Oct 30 (Wed), 7-9pm at LSB LT2. It will include topics covered up to (and including) the lectures on Oct 22. These include Problem Sets 1-3 and some of Problem Set 4. You can find sample midterms from previous years under the "Quizzes and Exams" section.
  • The numerical answers to Q1 of Problem Set 4 for S_1 is given by K=4/(1+4x^2+4y^2)^2 and H=4(1+2x^2+2y^2)/(1+4x^2+4y^2)^3/2. For Q2, H=0 and K=-sech^4 v.
  • Note that there is no lecture or tutorial on Nov 7 due to the Conferment of Bachelor’s Degrees and Master’s Degrees.
  • The midterm has been returned. The mean is 49, median is 53, with SD 13. You can collect the midterm from me at my office LSB 236 or after class next week.
  • Since the semester has ended early due to circumstances happening at CUHK, we will make announcement later about the arrangement for course assessment etc. at a later time.
  • Due to the shortening of Term 1 in 2019-20 and cancellation of the centralized final examination, we will use the following new assessment scheme for this course: Homework (20%) and Midterm (80%). Only Homework 1-4 will be counted towards the course grade.
  • You are still welcomed to submit HW 5 and HW 6 by email to me or the TA. The deadline for any homework submission is Dec 6, 2019 at 23:59pm. If you choose to submit HW 5/6, your scores toward Homework (20%) will be scaled accordingly. For example, if you submit all HW 1-4, you receive 20%. If you submit HW 1-3, and then HW 5-6, you receive 16.7%.
  • New update: For the homework assessment, only the 4 best homework out of the total of 6 will be counted.
  • University has just announced the options for late-drop and Pass/Fail grading. Deadline on Dec 10 (Tue). Apply directly to RES. Please see RES webpage "" for detail. Please also see a summary on concerns need to be considered for choosing these options on the departmental website

General Information


  • LI Man-chun Martin
    • Office: LSB 236
    • Tel: 3943-1851
    • Email:
    • Office Hours: by appointment

Teaching Assistant

  • CHEN Shanjiang
    • Office: LSB 222A
    • Tel: 3943-3575
    • Email:
    • Office Hours: Tue 9am-12pm; Wed 9am-12pm; Thur 9:30am-12pm

Time and Venue

  • Lecture: Tue 8:30-10:15AM at LSB LT4; Thur 9:30-10:15AM at LSB C2
  • Tutorial: Thur 8:30-9:15AM at LSB C2

Course Description

This course covers basic theory on curves, and surfaces in the Euclidean three space. Topics include: regular curves, Frenet formulas, local theory of curves, global properties of curves such as isoperimetric inequality, regular surfaces, 1st and 2nd fundamental form, Gaussian curvature and mean curvature, Gauss map, special surfaces such as ruled surfaces, surfaces of revolution, minimal surfaces, intrinsic geometry: geodesic, and Gauss-Bonnet Theorem. Students taking this course are expected to have knowledge in advanced calculus, linear algebra, and elementary differential equations.


  • "Differential Geometry of Curves and Surfaces" by Manfredo do Carmo, Prentice Hall, 1976

Pre-class Notes

Class Notes

Tutorial Notes


Quizzes and Exams


Assessment Scheme

Homework 20%
Midterm (Oct 30, 7-9pm, LSB LT2) 80%

Useful Links

Honesty in Academic Work

The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:

and thereby help avoid any practice that would not be acceptable.

Assessment Policy

Last updated: December 01, 2019 11:05:49