# Riemannian geometry

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Related to Semi-Riemannian geometry: Riemannian metric

## Rie·mann·ian geometry

(rē-män′ē-ən)
n.
A non-Euclidean system of geometry based on the postulate that within a plane every pair of lines intersects.

[After Georg Friedrich Bernhard Riemann.]

## Riemannian geometry

n
(Mathematics) a branch of non-Euclidean geometry in which a line may have many parallels through a given point. It has a model on the surface of a sphere, with lines represented by great circles. Also called: elliptic geometry

## Riemann′ian geom′etry

n.
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.
[1915–20; after German.French.B. Riemann]
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 Riemannian geometry - (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"elliptic geometrymath, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangementnon-Euclidean geometry - (mathematics) geometry based on axioms different from Euclid's; "non-Euclidean geometries discard or replace one or more of the Euclidean axioms"
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