Definition:Parallel (Geometry)/Surfaces

Definition
Let $S_1$ and $S_2$ be surfaces in ordinary space.

Let $S_1$ and $S_2$ have the property that:


 * for every point $P$ on $S_1$, a normal vector passing through $P$ is also a normal vector to $S_2$

and:
 * for every point $Q$ on $S_2$, a normal vector passing through $Q$ is also a normal vector to $S_1$.

Then $S_1$ and $S_2$ are parallel.