Definition:Surface of Revolution/Definition 2
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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.
The surface of revolution is the subset $S_F \subseteq \R^3$ such that:
- $S_F = \set {\tuple {x, y, z} : \tuple {\sqrt{x^2 + y^2}, z} \in F}$
where $F$ is the generating curve of the surface of revolution.
Also see
- Results about surfaces of revolution can be found here.
Sources
- 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Methods for Constructing Riemannian Metrics