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# Riemannian geometry

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noun Geometry.

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.Compare hyperbolic geometry.

the differential geometry of a metric space that generalizes a Euclidean space.

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## Origin of Riemannian geometry

First recorded in 1915–20

## Words nearby Riemannian geometry

Riefenstahl, Riegel's pulse, Riegger, riel, Riemann, Riemannian geometry, Riemann integral, Riemann sphere, Riemann-Stieltjes integral, Riemann surface, riempie

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2022

## How to use Riemannian geometry in a sentence

## British Dictionary definitions for Riemannian geometry

Riemannian geometry

noun

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 circlesAlso called: elliptic geometry

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

## Scientific definitions for Riemannian geometry

Riemannian geometry

[ rē-män′ē-ən ]

A non-Euclidean system of geometry based on the postulate that within a plane every pair of lines intersects.

The American Heritage® Science Dictionary
Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.