- 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.
- the differential geometry of a metric space that generalizes a Euclidean space.
- 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
