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 so...
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one of the non-Euclidean geometries that completely rejects the validity of Euclid`s fifth postulate and modifies his second postulate. Simply ... [6 related articles]
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A mathematical framework for describing curved shapes of any dimension. Riemannian geometry, named after its pioneer, Bernhard Riemann, plays a central role in Einstein's description of spacetime in general relativity.
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a non-Euclidean geometry that studies curved surfaces and differentiable manifolds in higher dimensional spaces
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