Seonglae ChoA rule that defines the inner product of vectors at each point of a manifold, enabling calculation of lengths and angles on the manifold
Riemannian manifold
In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature are defined. Euclidean space, the -sphere, hyperbolic space, and smooth surfaces in three-dimensional space, such as ellipsoids and paraboloids, are all examples of Riemannian manifolds. Riemannian manifolds are named after German mathematician Bernhard Riemann, who first conceptualized them.
https://en.wikipedia.org/wiki/Riemannian_manifold
