Asymptotic lines of a parametrized surface

100 Views Asked by At

Prove that the lines $v=k\pi$ are asymptotic lines for the surface parametrized by $$\varphi:(0,\pi )\times\mathbb{R}\rightarrow\mathbb{R}^{3}$$ $$\varphi (u,v)=(v,\cos(u),\sin(v))$$

Honestly, I don't know how to proceed because the professor talk with us only about the $v$ or $u-lines$ like $\varphi (u_{0}+t,v)$, $t\in\mathbb{R}$

Can someone axplain this concept? Thanks before!

1

There are 1 best solutions below

4
On

According to your description, we can plot the function using Mathematica:enter image description here

I do not think it have any "asymptotic lines".