MATH5061 - Riemannian Geometry I - 2022/23

Announcement

• 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: https://cuhk.zoom.us/j/92286586250
• Take home Final: from 24 April to 28 April

General Information

Lecturer

• 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.

References

• 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 (https://drive.google.com/file/d/109aB5rqRfwEJlOnVQGZyG2H366dz0HA0/view)

Honesty in Academic Work

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and thereby help avoid any practice that would not be acceptable.