Definition:Generating Curve of Surface of Revolution

Definition

Let $H = \set {\tuple {x, y} : y \in \R_{> 0}} \subset \R^2$ be the open upper half-plane.

Let $F \subset H$ be a $1$-dimensional embedded submanifold.

Let $S_F$ be a surface of revolution.

Then $F$ is called the generating curve of $S_F$.

Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Methods for Constructing Riemannian Metrics