Definition:Curvilinear Coordinate Surface

Definition
Let $\KK$ be a curvilinear coordinate system in $3$-space.

Let $\QQ_1$, $\QQ_2$ and $\QQ_3$ denote the one-parameter families that define $\KK$.

Each of the surfaces which is an element of $\QQ_i$ is known as a curvilinear coordinate surface.

Each curvilinear coordinate surface has its unique $q_i$ which is constant for that surface.