Riemannian Geometry
- is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point that varies smoothly from point to point
- this gives, in particular, local notions of angle, length of curves, surface area, and volume
- from those, some other global quantities can be derived by integrating local contributions