Announcement

• Problem Set 6, the last one, is posted and the due date is Apr 21 (Wed).
• The online course and teaching evaluation (OCTE) will be available from Apr 14, 2:30PM. Please be reminded to submit your answers by Apr 15, 5:15PM.
• Final Exam will be a take-home exam conducted online via email and Blackboard. It will be available on April 28, 2021 at 2:30PM and the submission deadline (via email or Blackboard) will be May 5 at 2:30PM. Your submitted solution will be checked carefully to avoid plagiarism. Discussions amongst classmates are strictly prohibited.
• Problem Set 5 is posted and the due date is Apr 7 (Wed).
• Question 4 in Problem Set 4 is modified slightly.
• The due date of Problem Set 4 is postponed to Mar 24.
• Problem Set 4 is posted and the due date is Mar 17 (Wed).
• There is a revision of Question 2 in Problem Set 3.
• Problem Set 3 is posted and the due date is Mar 3 (Wed).
• There is a revision of Question 5 in Problem Set 2.
• Problem Set 2 is posted and the due date is Feb 10 (Wed).
• Problem Set 1 is posted and the due date is Jan 27 (Wed). Please submit your assignment via Blackboard.
• The first lecture will be on Jan 13 (Wed) from 2:30 to 5:15pm. If you are not yet official registered on CUSIS or a student sitting in this course, please send me an email to let me know so that I can keep you updated about the course via emails (and send you the ZOOM passcodes).
• General course arrangements:
  • In view of the current pandemic situation, this course will be 100% online until further notice. Please keep checking the course webpage for any new updates about the course. We will be using a combination of (i) Course Webpage (for course materials); (ii) ZOOM (for lectures and appointments); (iii) Blackboard/Gradescope (for lecture videos, homework/tests submission).
  • Each lecture will be a ZOOM "Meeting" hosted by the instructor, taking place during the same time as they have normally been scheduled. The particulars of the meetings are as follow:
    • Lecture ID: 928-2173-5090
    Alternatively, you can also click on the corresponding links under the "Useful Links" section below. Lectures will be recorded and uploaded to Blackboard in a folder under “Panopto Video”.
  • For homework assignments, you can either type up your assignment or scan a copy of your written assignment into ONE PDF file and submit through CUHK Blackboard on/before the due date. Please remember to write down your name and student ID. You can refer to the webpage under "Useful Links" below about how to submit assignments through Blackboard.
  • If you have any questions, you can stay in the ZOOM meeting after class or you can email me or the TAs to set up an appointment for a future ZOOM meeting.

General Information

Lecturer

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

Teaching Assistant

• WANG, Gaoming
  • Office: LSB 222A
  • Tel: 3943-3575
  • Email:
  • Office Hours: Tue 3:30-5:30PM (or by appointment) - ZOOM Meeting ID: 987-0161-0174

Time and Venue

• Lecture: Wed 2:30-5:15PM (online via ZOOM)

Course Description

This course is intended to provide a solid background in Riemannian Geometry. Topics include: affine connection, tensor calculus, Riemannian metric, geodesics, curvature tensor, completeness and some global theory. Students taking this course are expected to have knowledge in differential geometry of curves and surfaces.

References

• "Lectures on Differential Geometry" by S.S. Chern, W.H. Chen & K.S. Lam
• "Riemannian Geometry" by M. do Carmo
• "Riemannian Geometry" by S. Gallot, D. Hulin & J. Lafontaine
• "Riemannian Geometry and Geometric Analysis" by J. Jost
• "Riemannian Manifolds: An Introduction to Curvature" by J. M. Lee

Lecture Notes

• Lecture 1 on Jan 13
• Lecture 2 on Jan 20
• Lecture 3 on Jan 27
• Lecture 4 on Feb 3
• Lecture 5 on Feb 10
• Lecture 6 on Feb 24
• Lecture 7 on Mar 3
• Lecture 8 on Mar 10
• Lecture 9 on Mar 17
• Lecture 10 on Mar 24
• Lecture 11 on Mar 31
• Lecture 12 on Apr 7
• Lecture 13 on Apr 14
• Lecture 14 on Apr 21

Assignments

• Problem Set 1 (due on Jan 27)
• Problem Set 2 (due on Feb 10) - revised on Feb 4
• Problem Set 3 (due on Mar 3) - revised on Feb 28
• Problem Set 4 (due on Mar 17 Mar 24) - revised on Mar 19
• Problem Set 5 (due on Apr 7)
• Problem Set 6 (due on Apr 21)

Solutions

• Solution to Problem Set 1
• Solution to Problem Set 2
• Solution to Problem Set 3
• Solution to Problem Set 4
• Solution to Problem Set 5
• Solution to Problem Set 6

Assessment Scheme

Useful Links

• How to submit assignments through CUHK Blackboard
• Link to ZOOM meeting for Lectures

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.