# Riemannian 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.

## Origin of Riemannian geometry^{}

First recorded in 1915–20

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# Riemannian 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 circlesAlso called: elliptic geometry

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
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# 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.

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