Riemannian Geometry

Between February and November 2023, I assisted Dr Hwee Kuan Lee in teaching a course on differential geometry to AI researchers in Singapore’s Agency for Science Technology and Research.

We covered the following topics over a period of about 8 months:

• Vectors, one forms/covectors,
• Covariant and contravariant tensors, Christoffel symbols, the metric tensor
• Differentiable manifolds, charts, tangent plane/bundle, vector fields
• The covariant derivative, parallel transport, and the geodesic
• Pushforwards and pullbacks of vectors, one forms and tensors
• Flow, Lie derivative, Lie bracket