another way to see meridians and parallel are geodesic

Question

i'm having trouble with this particular question from Andrew Pressley Elementary Differential Geometry, second edition

"There is another way to see that all the meridians, and all the parallels corresponding to stationary points of f, are geodesics on a surface of revolution. What is it ?"

the solution said they are normal section, but is it enough that i prove normal section is geodesic?

thanks before

Answer 1

The meridians are geodesics ok, but not parallel lines ( excluding the special case of the central equator) which please check whether I got it right.

Parallels are made not by normal sections, there is an angle between surface normal and arc normal. Normal sections are not geodesics and geodesic curvature is non-zero.