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. Cf. hyperbolic geometry.
2. the differential geometry of a metric space that generalizes a Euclidean space.
Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease.