Riemannian geometry

  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.: Compare hyperbolic geometry.

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

Origin of Riemannian geometry

First recorded in 1915–20

Words Nearby Riemannian geometry

Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2023

British Dictionary definitions for Riemannian geometry

Riemannian geometry

  1. 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

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 ]

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

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