Riemannian
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Riemannian geometry — [rē män′ē ən] n. [after G. F. B. Riemann (1826 66), Ger mathematician] a form of non Euclidean geometry in which there are no parallel lines, since its figures can be conceived as constructed on a curved surface where all straight lines intersect … English World dictionary
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
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
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 circle — In metric space theory and Riemannian geometry, the term Riemannian circle refers to a great circle equipped with its great circle distance. In more detail, the term refers to the circle equipped with its intrinsic Riemannian metric of a compact… … 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 Penrose inequality — In mathematical general relativity, the Penrose inequality, first conjectured by Sir Roger Penrose, estimates the mass of a spacetime in terms of the total area of its black holes and is a generalization of the positive mass theorem. The… … 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
Riemannian geometry — Geom. 1. Also called elliptic geometry. the branch of non Euclidean geometry that replaces the parallel postulate of Euclidean geometry with the postulate that in a plane every pair of distinct lines intersects. Cf. hyperbolic geometry. 2. the… … Universalium
Riemannian manifold — noun 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 … Wiktionary
Riemannian geometry — noun the branch of differential geometry that studies Riemannian manifolds … Wiktionary
