The parallel postulate in Euclidean geometry states, for two dimensions, that given a line l and a point P not on l, there is exactly one line through P that does not intersect l, i.e., that is ...

A case-study in non-Euclidian geometry.Wikipedia But even though they are curving we see that at one point the lines are parallel at a point. If you have forgotten your basic geometry, parallel ...

Complex hyperbolic space: A non-Euclidean space equipped with a complex structure and constant negative curvature, forming the central subject of complex hyperbolic geometry.

Two main possibilities then arise: one is spherical geometry, in which parallel lines can eventually touch, in the way that Earth’s meridians cross at the poles; the other is hyperbolic geometry ...

Complex hyperbolic geometry investigates spaces that combine the subtleties of complex structures with non‐Euclidean, negatively curved metrics, offering rich terrain for both theoretical ...