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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
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-mänē-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.
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