Behavior of lines with a common perpendicular in each of the three types of geometry

# In Euclidean geometry the lines remain at a constant distance from each other, and are known as parallels.

# In hyperbolic geometry they "curve away" from each other, increasing in distance as one moves further from the points of intersection with the common perpendicular; these lines are often called ultraparallels.

non-Euclidean geometry is characterized by a non-vanishing Riemann curvature tensor.