@XanderHenderson Well, I'm working on classifying ruled Weingarten surfaces in Thurston model geometries and this curve came up to be important in the case of the product space $\mathbb{H}^2\times \mathbb{R}$ just as the helix $(\cos t, \sin t, t)$ was important for $\mathbb{S}^2\times \mathbb{R}$. Part of me wants to call it "hyperbolic helix", but looking at the curve trace that seems really outrageous... Can't think of any other name
*Edit: the helix is also important for the Heisenberg group $\mathrm{Nil}_3$ space
