Keywords

#riemannian_manifold

Riemannian manifold

Smooth manifold with an inner product on each tangent space

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.

Sun 8th

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Riemannian manifold Pseudo-Riemannian manifold Riemannian geometry Curvature of Riemannian manifolds Sub-Riemannian manifold Manifold Ricci-flat manifold Geodesic Riemann curvature tensor Exponential map (Riemannian geometry)
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