MATH5061  Riemannian Geometry I  2023/24
Announcement
 The final written examination will take place inclass on Apr 22 (Mon), 2024 from 2:30PM  5:00PM.
 Problem Set 5 (the last one) is posted and due on Apr 15.
 Problem Set 4 is posted and due on Mar 25.
 Problem Set 3 is posted and due on Mar 11.
 Problem Set 2 is posted and due on Feb 26.
 The lecture on Jan 29 will take place at LSB 219.
 Problem Set 1 is posted and due on Feb 5.
 The first class will be on Jan 8, 2024. Note that the class on Jan 15 will be cancelled.
General Information
Lecturer

LI Manchun Martin
 Office: LSB 236
 Tel: 39431851
 Email:
 Office Hours: By appointment
Time and Venue
 Lecture: Mon 2:30PM5:15PM at 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.
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
Preclass Notes
Lecture Notes
 L1  Abstract manifolds and submanifolds
 L2  Tangent bundles and vector fields
 L3  Tensors and Lie derivative
 L4  Differential forms
 L5  Riemannian metrics and connection
 L6  Geodesics and exponential map
 L7  Riemann Curvature Tensor
 L8  Submanifold theory
 L9  First and second variation formula for curves
 L10  Jacobi fields
 L11  Conjugate points and minimizing geodesics
 L12  Completeness of Riemannian manifolds
 L13  Bonnet Myers and Cartan Hadamard Theorem
 L14  Space forms
 L15  Comparison theorems in Riemannian geometry
Assignments
 Problem Set 1 (due on Feb 5)
 Problem Set 2 (due on Feb 26)
 Problem Set 3 (due on Mar 11)
 Problem Set 4 (due on Mar 25)
 Problem Set 5 (due on Apr 15)
Solutions
 Solutions to Assignment 1
 Solutions to Assignment 2
 Solutions to Assignment 3
 Solutions to Assignment 4
 Solutions to Assignment 5
Assessment Scheme
Homework Assignments  50%  
Final Examination (inclass on Apr 22, 2024)  50% 
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 08, 2024 23:14:04