a form of non-Euclidean geometry in which there are no parallel lines, since its figures can be conceived as constructed on a curved surface where all straight lines intersect, and in which the sum of the angles of a triangle exceeds 180°
See Riemannian geometry in American Heritage Dictionary 4
(rē-mänˈē-ən)
noun
A non-Euclidean system of geometry based on the postulate that within a plane every pair of lines intersects.