Tasks for expert:
- completely rewrite, bearing in mind applications in physics
- better discussion of 2,3,4+ dimensions, e.g. properties of metric tensor special to low dimensions
- clarify Riemannian versus semi-Riemannian manifolds
- clarify flat versus nonflat spaces, spacetimes
- better examples (give range of coordinates, specify whether any functions used are arbitrary smooth or whatever)
Tasks for anyone:
- improve diction
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