I've been playing around trying to understand curved spaces by reinventing the maths involved. The maths and source are up at https://github.com/simon-frankau/curved-spaces/, and if you wait for the giant pile of Rust WASM to download you can also just play with it at https://arbitrary.name/curved-space. I won't write more here, since I documented a fair amount of what I worked through in the README.md
Posted 2024-06-05.