MATH5061 - Riemannian Geometry I - 2019/20

Course Name: 
Course Year: 


  • Problem Set 6 has been revised and the new due date is May 1. The last question is now optional.
  • The last Problem Set 6 is posted and the due date is Apr 29 (Wed).
  • Due to potential security issues, we have revised the passwords for all the ZOOM meetings. Please check you email to receive the new passwords.
  • The online course and teaching evaluation (OCTE) will be available from Apr 22, 2:30PM. Please be reminded to submit your answers by Apr 23, 5:15PM.
  • Problem Set 5 is posted and the due date is Apr 15 (Wed).
  • Final Exam will be a take-home exam conducted online via email and Blackboard. It will be available on May 6, 2020 at 2:30PM and the submission deadline (via email or Blackboard) will be May 13 at 2:30PM. Your submitted solution will be checked carefully to avoid plagiarism. Discussions amongst classmates are strictly prohibited.
  • Problem Set 4 is posted and the due date is Apr 1 (Wed).
  • Problem Set 3 is posted and the due date is Mar 18 (Wed).
  • The revised due date for Problem Set 2 is Mar 4.
  • Special announcement on the course arrangements:
    • To reduce the risk of spreading the novel coronavirus, the university has announced to provide online teaching starting from 17 February 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 (for lecture videos and Q&A).
    • 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 (Wed 2:30-5:15PM) ID: 431-432-756
      Alternatively, you can also click on the corresponding links under the "Useful Links" section below (using the same passwords as above). Please try your best to get familiar with various built-in functions (especially “Raise Hand”, “Chat” and “Private Message” functions) in ZOOM. Lectures will be recorded and uploaded to Blackboard in a folder under “Panopto Video”.
    • For homework assignments, please do NOT come to campus to submit your completed assignments. Instead, you can either type up your assignment or scan a copy of your written assignment into ONE PDF file and send it to me by email on/before the due date. Please remember to write down your name and student ID.
    • If you have any questions, you can stay in the ZOOM meeting after class or you can email me to set up an appointment for a future ZOOM meeting. You are also highly encouraged to use the "Discussion Board" in Blackboard as well. Anyone of you are welcomed to ask and answer questions posted there, I will be regularly checking and replying some of the posts myself as well.
  • Problem set 1 has been revised. Some hints are added to Question 1.
  • Problem Set 2 is posted and the due date is Feb 19 (Wed).
  • Problem Set 1 is posted and the due date is Jan 22 (Wed).
  • The first lecture will be on Jan 8 (Wed) from 2:30 to 5:15pm at LSB 222.

General Information


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

Time and Venue

  • Lecture: Wed 2:30-5:15PM, LSB 222

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.


  • "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 Manifolds: An Introduction to Curvature" by J. M. Lee
  • "Riemannian Geometry and Geometric Analysis" by J. Jost

Lecture Notes



Assessment Scheme

Homework 50%
Take-home final 50%

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: April 29, 2020 18:19:54