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Riemannian geometry reading group

Jan 8 2022 · 2 min read

This is the page for the Riemannian Geometry reading group I’m organizing for the winter of 2022. The idea is to explore some basic concepts first to get everyone up to speed, then branch out into more material later on. Below is a list of material along with the week number in which I’d like to get to it, though just the first few weeks for now. I’ll be updating it as we go along.

Schedule

Week Content Reference 1 Reference 2 Reference 3
1 Tensors, Review of Diff Geo LeeRM Ch 2-3 Warner Ch 2, G&Q1 Ch14 Kb&N1 Ch 1.1-1.3 Ch 4.1
2 Metrics, Covariant Derivatives / Connections, Geodesics LeeRM Ch 3-4 G&Q1 Ch 15
2.5 Geodesics, Riemannian Distances, Hopf-Rinow Theorem LeeRM Ch 5-6 G&Q1 16 Kb&N1 3.6, 4.1-4.5
3 Curvature and beyond LeeRM Ch 7-8 G&Q1 Chapter 17-18

Notes

Legend

Along with a legend of books:

Short Title Full Title Authors
LeeRM Introduction to Riemannian Manifolds 2nd Edition John Lee
LeeSM Introduction to Smooth Manifolds 3rd Edition John Lee
G&Q1 Differential Geometry and Lie Groups: A first course Jean Gallier, Jocelyn Quaintance
G&Q2 Differential Geometry and Lie Groups: A second course Jean Gallier, Jocelyn Quaintance
Warner Foundations of Differentiable Manifolds and Lie Groups Frank Warner
Kb&N1 Foundations of Differential Geometry Vol 1 Shoshichi Kobayashi, Katsumi Nomizu
Kb&N2 Foundations of Differential Geometry Vol 2 Shoshichi Kobayashi, Katsumi Nomizu

Other Topics

Some other cool stuff I’d like to cover eventually: