Riemannian geometry
noun Etymology: G. F. B. Riemann Date: 1896 a non-Euclidean geometry in which straight lines are geodesics and in which the parallel postulate is replaced by the postulate that every pair of straight lines intersects

New Collegiate Dictionary. 2001.

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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 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 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 geometry — noun the branch of differential geometry that studies Riemannian manifolds …   Wiktionary

  • Riemannian geometry — noun (mathematics) a non Euclidean geometry that regards space as like a sphere and a line as like a great circle Bernhard Riemann pioneered elliptic geometry • Syn: ↑elliptic geometry • Topics: ↑mathematics, ↑math, ↑maths …   Useful english dictionary

  • Riemannian geometry — Riemann′ian geom′etry n. math. 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 • Etymology: 1915–20; after G.F.B. Riemann …   From formal English to slang

  • Fundamental theorem of Riemannian geometry — In Riemannian geometry, the fundamental theorem of Riemannian geometry states that on any Riemannian manifold (or pseudo Riemannian manifold) there is a unique torsion free metric connection, called the Levi Civita connection of the given metric …   Wikipedia

  • Gauss's lemma (Riemannian geometry) — In Riemannian geometry, Gauss s lemma asserts that any sufficiently small sphere centered at a point in a Riemannian manifold is perpendicular to every geodesic through the point. More formally, let M be a Riemannian manifold, equipped with its… …   Wikipedia

  • List of formulas in Riemannian geometry — This is a list of formulas encountered in Riemannian geometry.Christoffel symbols, covariant derivativeIn a smooth coordinate chart, the Christoffel symbols are given by::Gamma {ij}^m=frac12 g^{km} left( frac{partial}{partial x^i} g {kj}… …   Wikipedia

  • Isometry (Riemannian geometry) — In the study of Riemannian geometry in mathematics, a local isometry from one (pseudo )Riemannian manifold to another is a map which pulls back the metric tensor on the second manifold to the metric tensor on the first. When such a map is also a… …   Wikipedia

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