MATH5061  Riemannian Geometry I  2020/21
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 takehome 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: 92821735090
 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, Manchun Martin
 Office: LSB 236
 Tel: 39431851
 Email:
 Office Hours: By appointment
Teaching Assistant

WANG, Gaoming
 Office: LSB 222A
 Tel: 39433575
 Email:
 Office Hours: Tue 3:305:30PM (or by appointment)  ZOOM Meeting ID: 98701610174
Time and Venue
 Lecture: Wed 2:305:15PM (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 17Mar 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
Homework  50%  
Takehome final (available on Apr 28)  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:
http://www.cuhk.edu.hk/policy/academichonesty/and thereby help avoid any practice that would not be acceptable.
Assessment Policy Last updated: April 21, 2021 17:10:11