411 REFERENCE · Wikibooks
Differentiable Manifolds/Riemannian manifolds
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Riemannian metric Let be a -differentiable manifold. A Riemannian metric on is a collection of inner products
such that the components of the matrix of are contained within .
Riemannian manifold A Riemannian manifold is a pair , where is a differentiable manifold and a Riemannian metric on .
Path length on Riemannian differentiable manifolds