Definition:Meridian of Surface of Revolution

Definition

Let $S_C$ be a surface of revolution.

Let its smooth local parametrization be of the form:

$\map X {t, \theta} = \tuple {\map y t \cos \theta, \map y t \sin \theta, \map x t}$

Then the $t$-coordinate curves $t \mapsto \map X {t, \theta_0}$ are called the meridians of $S_C$.

Also see

• Definition:Meridian

Sources

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