Riemannian geometry

American  

noun

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.

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

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Riemannian geometry British  

noun

1. Also called: elliptic geometry.  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

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Riemannian geometry Scientific  

/ rē-män′ē-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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Etymology

Origin of Riemannian geometry

First recorded in 1915–20

Example Sentences

Handily for Einstein, though, an old university chum, Marcel Grossmann, was an expert in Riemannian geometry, a piece of previously pure mathematics created to describe curved multi-dimensional surfaces.

From Economist • Nov. 25, 2015

Take the edge dislocations wandering through the crystal, and you find you get Riemannian geometry.

From Scientific American • Nov. 5, 2013