Homework Differential Geometry Of Curves


Your course grade will be determined on the following basis:
Midterm Exam30%
Final Exam40%

When computing your homework grade, the lowest weekly homework score will be dropped, and the remaining scores will be averaged with your challenge problem scores. (That is, each challenge problem is worth as much as a weekly homework assignment!)



Unless otherwise noted, all reading assignments refer to the textbook, Differential Geometry of Curves and Surfaces by Manfredo do Carmo.
Date Reading
Nov 5Sections 4.4-4.5
Oct 27Sections 3.5 and 4.1-4.3
Oct 18Sections 3.1-3.3 and chapter 3 appendix
Oct 6Sections 2.5-2.6
Sep 27Section 2.4
Sep 20Section 2.3 and chapter 2 appendix
Sep 13Sections 2.1-2.2
Aug 23Chapter 1


The list of homework problems was last updated on Monday, November 22. The most recently assigned problems are shown in green.
Hwk # Due Problems
14** not collected ** Section 4.6: 1,2,4,5
13Wed, Dec 1Problems from Lecture 39.
12Mon, Nov 22Problem from Lecture 36.
Section 4.4: 20a
11Mon, Nov 15 Section 4.3: 3, 9
Section 4.4: 1, 2, 5, 8
10Mon, Nov 8 Section 3.5: 3
Section 4.3: 1, 2, 5, 8
9Mon, Nov 1 Section 3.2: 2, 5, 17
Section 3.3: 5, 6, 20
8Mon, Oct 25 Section 2.5: 7, 9, 10, 12
Section 3.2: 3, 8
7Mon, Oct 11 Section 2.3: 1, 4
Section 2.4: 1, 3, 12, 15, 20
6Mon, Oct 4Problems from Lecture 15.
Section 2.2: 17 (Hint: Read section 2.3)
5Mon, Sep 27 Section 2.2: 1, 2, 3, 5
4Mon, Sep 20Problem from Lecture 10.
Problems from Lecture 9.
3Mon, Sep 13Problems from Lecture 7.
Problem from Lecture 8.
2Wed, Sep 8Additional problems from Lecture 5.
Section 1.5: 5, 12, 14
1Mon, Aug 30 This corrected version of problem 4 from section 1.3.
Section 1.4: 8
Section 1.5: 2, 4, 7

Online Resources

These online tools (java applets, etc.) complement the material from the textbook and lectures.

Up: Home page of David Dumas


  • Tutorial will begin on Sep 10.
  • Homework 1 is posted and due on Sep 15 at 5PM.
  • The lecture notes is posted. Please note that the lecture notes will be revised continuously as the class goes on.
  • Homework 2 is posted and due on Sep 23 (Wed) at 5PM.
  • Midterm 1 will take place in the second half of the class next Tuesday (Sep 22). It will cover all the materials up to and including the lectures and tutorials this Thursday (Sep 17). There will still be lecture in the first half of the class before the midterm.
  • Homework 2 typo: #5, the power on the right hand side should be "n-i" instead of "n-1".
  • Homework 3 is posted.
  • The statistics for midterm 1 is as follows: mean=11.05, median=11, highest=16, standard deviation=3.23. If you have not got back your midterm, please come to my office to pick it up.
  • Homework 4 is posted.
  • There is a mistake in HW4 Q2 (b). The revised version has been uploaded.
  • Midterm 2 is changed to Oct 27 (Tuesday) in class. Please make sure to attend the midterm.
  • Homework 5 is posted.
  • The due date of Homework 5 is postponed to Oct 15.
  • For question 2 in HW5, the curve is arc-length parametrized. The revised version has been uploaded.
  • Homework 6 is posted.
  • In HW5 Suggested Exercise 1(a), the sign in front of epsilon should be "plus". The revised version has been uploaded.
  • Homework 7 & 8 are posted. Please note that HW 7 is due on Wednesday, the day after midterm 2.
  • Midterm 2 will be held in class on Oct 27, 10:30-11:30AM. There will be no lecture on that day. The test will cover all the materials up to and including the lecture on Oct 22.
  • In Q.1 of Homework 6, there should be no "squared" of the integrand. The revised version has been uploaded.
  • Homework 9 is posted.
  • Midterm 2 has been returned in class today. Here are the statistics: mean = 17.3, median = 18, standard deviation = 2.63. If you missed class today, please come to my office to pick up your midterm.
  • In suggested solution to HW 7 Q.3(b), the semi-circles need to be reparametrized suitably to satisfy the geodesic equations.
  • The final exam has been scheduled on Dec 15, 2015 (Tuesday) 9:30am - 12:00pm at Indoor Multi-purpose Sports Hall, Shaw College. Please refer to the RGS webpage for the most up-to-date information.
  • Homework 10 is posted.
  • The last homework assignment 11 is posted. Please note that the due date is on Nov 26, Thursday.

General Information


  • Li Man-chun Martin
    • Office: LSB 236
    • Tel: 3943-1851
    • Email:

Teaching Assistant

  • Huang Shaochuang
    • Office: LSB 222A
    • Tel: 3943-3575
    • Email:
    • Office Hours: Tu 1:30-6:15PM, W 8:30AM-12:15PM, F 8:30AM-12:15PM
  • Wang Qizhi
    • Office: LSB 233
    • Tel: 3943-7957
    • Email:
    • Office Hours: M 2:30-5:00PM, W 2:30-5:00PM, F 8:30AM-12:00PM

Time and Venue

  • Lecture: Tu 10:30AM - 12:15PM, LSB C2; Th 10:30AM - 11:15AM, LSB C2
  • Tutorial: Th 11:30AM - 12:15PM, 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: Curves - Surfaces - Manifolds" (2nd edition) by Wolfgang Kuhnel


  • "Differential Geometry of Curves and Surfaces" by Manfredo do Carmo
  • "Differential Forms and Applications" by Manfredo do Carmo

Pre-class Notes

Lecture Notes

Tutorial Notes



Assessment Scheme

Weekly Homework Assignment 10%
Midterms (Sep 22 and Oct 27) 40%
Final Exam (Dec 15 9:30AM-12:00PM, please refer to RGS's webpage for the most updated information) 50%

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.

Last updated: December 03, 2015 13:40:00

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