- Riemannian manifold
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in Riemannian geometry, a real differentiable manifold M in which each tangent space is equipped with an inner product g, a Riemannian metric, in a manner which varies smoothly from point to point.
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Riemannian manifold
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Riemannian manifold — In Riemannian geometry, a Riemannian manifold ( M , g ) (with Riemannian metric g ) is a real differentiable manifold M in which each tangent space is equipped with an inner product g in a manner which varies smoothly from point to point. The… … Wikipedia
Pseudo-Riemannian manifold — In differential geometry, a pseudo Riemannian manifold (also called a semi Riemannian manifold) is a generalization of a Riemannian manifold. It is one of many things named after Bernhard Riemann. The key difference between the two is that on a… … Wikipedia
Sub-Riemannian manifold — In mathematics, a sub Riemannian manifold is a certain type of generalization of a Riemannian manifold. Roughly speaking, to measure distances in a sub Riemannian manifold,you are allowed to go only along curves tangent to so called horizontal… … Wikipedia
Cut locus (Riemannian manifold) — In Riemannian geometry, the cut locus of a point p in a manifold is roughly the set of all other points for which there are multiple minimizing geodesics connecting them from p, but it may contain additional points where the minimizing geodesic… … Wikipedia
pseudo-Riemannian manifold — noun in differential geometry, a generalization of a Riemannian manifold Syn: semi Riemannian manifold … Wiktionary
Riemannian geometry — Elliptic geometry is also sometimes called Riemannian geometry. 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… … Wikipedia
Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… … Wikipedia
Riemannian submersion — In differential geometry, a branch of mathematics, a Riemannian submersion is a submersion from one Riemannian manifold to another that respects the metrics, meaning that it is an orthogonal projection on tangent spaces. Let (M, g) and (N, h) be… … Wikipedia
Riemannian connection on a surface — For the classical approach to the geometry of surfaces, see Differential geometry of surfaces. In mathematics, the Riemannian connection on a surface or Riemannian 2 manifold refers to several intrinsic geometric structures discovered by Tullio… … Wikipedia
Riemannian submanifold — A Riemannian submanifold N of a Riemannian manifold M is a smooth manifoldequipped with the induced Riemannian metric from M . The image of an isometric immersion is a Riemannian submanifold … Wikipedia
