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