# MATH4030 - Differential Geometry - 2016/17

Course Name:
Course Year:
2016/17
Term:
1

### Announcement

• (Dec 8) Solution to Homework 11 is posted.
• (Dec 1) The final exam will be held on Dec 15, 2016, 9:30am - 12pm at New Asia College Gymnasium. It will cover everything from the first lecture up to and including the lecture on Nov 29, and all the assignments. Please remember to bring your student ID to the exam. (Note: The Gauss and Codazzi equations will be given in the exam so you do not have to memorize them.)
• (Nov 29) The deadline for Homework 11 is extended to Dec 6 at 5PM.
• (Nov 23) Solution to Homework 10 is posted.
• (Nov 22) The last Homework 11 is posted and it is due on Dec 1 (Thurs) at 5PM.
• (Nov 17) Solution to Homework 9 is posted.
• (Nov 15) Homework 10 is posted and it is due on Nov 22 (Tue) at 5PM.
• (Nov 10) Solution to Homework 8 is posted.
• (Nov 8) Homework 9 is posted and it is due on Nov 15 (Tue) at 5PM.
• (Nov 3) Q.4 in Homework 8 has be corrected (Thanks to Wong Wing Hong for pointing out the mistake.)
• (Nov 3) Solution to Homework 7 is posted.
• (Nov 1) Homework 8 is posted and it is due on Nov 8 (Tue) at 5PM.
• (Oct 27) Solution to Homework 6 is posted.
• (Oct 25) Homework 7 is posted and it is due on Nov 1 (Tue) at 5PM.
• (Oct 25) Midterm has been returned after class today. Here are the statistics: max=39, mean=27.3, median=28, standard deviation=8.08. If you missed class today, please pick it up from me after class on Thursday.
• (Oct 18) Homework 6 is posted and it is due on Oct 25 (Tue) at 5PM.
• (Oct 12) Solution to Homework 5 is posted.
• (Oct 11) There is no homework posted this week in view of the coming midterm on Thursday.
• (Oct 6) Solution to Homework 4 is posted.
• (Oct 6) The midterm will be on Oct 13 in class (10:30am-12pm, LSB C2). It will cover materials up to and including the lecture on Oct 6 (excluding the differential topology of surfaces).
• (Oct 4) Homework 5 is posted and it is due on Oct 11 (Tue) at 5PM.
• (Sep 29) Solution to Homework 3 is posted.
• (Sep 27) Homework 4 is posted and it is due on Oct 4 (Tue) at 5PM.
• (Sep 22) Solution to Homework 2 is posted.
• (Sep 20) Homework 3 is posted and it is due on Sep 27 (Tue) at 5PM.
• (Sep 19) Solution to Homework 1 is posted.
• (Sep 13) Homework 2 is posted and it is due on Sep 20 (Tue) at 5PM.
• (Sep 7) Homework 1 has been revised.
• (Sep 6) Homework 1 is posted and it is due on Sep 13 (Tue) at 5PM.
• (Sep 6) There will no tutorial class in the first week. The first tutorial will begin on Sep 15.

### General Information

#### Lecturer

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

#### Teaching Assistant

• CHAU Chi Fai
• Office: LSB 222B
• Tel: 3943 7963
• Email:
• Office Hours: Mon 8:30-11:30AM; Tue 8:30-10:30AM; Thurs 8:30-10:30AM, 1:30-2:30PM

#### 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.

### Textbooks

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

### References

• "Curves and Surfaces (2nd ed)" by S. Montiel and A. Ros, Graduate Studies in Mathematics, Vol.69, American Mathematical Society, 2009
• "Differential Geometry: Curves - Surfaces - Manifolds (2nd ed)" by W. Kuhnel, Student Mathematical Library, Vol.16, American Mathematical Society 2005
• "Differential Forms and Applications" by M. do Carmo, Universitext, Springer-Verlag 1998

### Assessment Scheme

 Homework 10% Midterm (Oct 13, in class) 40% Final Exam 50%