Riemannian geometry

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

Riemannian geometry

noun

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 calledelliptic geometry

Riemannian geometry

/ rē-män′ē-ən /

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

Word History and Origins

Origin of Riemannian geometry¹

First recorded in 1915–20

Example Sentences

It belongs to the field of Riemannian geometry, the modern theory of curved spaces with any number of dimensions.

From Nature

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

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

From Scientific American

The mathematical machinery of Riemannian geometry goes much further and actually gives you a way to define and calculate numerical measures of curvature—not to just say if there is some or none.

From Scientific American