MATH5061 - Riemannian Geometry I - 2022/23

Course Name: 
Course Year: 


  • assessment scheme: 40% (Midterm)+60% (Final)
  • Take home Midterm: from 27 March to 31 March
  • Midterm period: no class on 29 March
  • Lecture at 8 March at zoom:
  • Take home Final: from 24 April to 28 April

General Information


  • Lee, Man-Chun
    • Office: LSB 237
    • Tel: 3943 5137
    • Email:

Time and Venue

  • Lecture: LSB 222, Wed 10:30-13:15

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.


  • Manfredo do Carmo: Riemannian Geometry
  • Jeff Cheeger and David G. Ebin: Comparison Theorems in Riemannian Geometry
  • Peter Li: Lecture notes on geometric analysis
  • Petersen: Riemannian Geometry
  • T. Frankel: The Geometry of Physics

Lecture Notes

  • sub-manifold
  • sources of variational formula for sub-manifold: lecture note by Xin Zhou (

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: March 16, 2023 09:33:12