I am trying to solve the following question:
Show that for a surface given by revolving the curve (x(u),0,u) around the z-axis, the meridians are geodesics.
Firstly, I am trying to get a visual picture for the function (x(u),0,u). So I am seeing the function as x=z, which gives a line through the origin, and if I rotate it about the z-axis then it should be a cone? Is this correct?
After that I should paramatise the surface? Am I heading in the right direction?