Revolving the unit speed curve c(u)=(g(u),h(u),0) about the x-axis

produces a surface which can be covered by the coordinate patch

PHI(u,v)=(g(u),h(u)cosv,h(u)sinv)

Assume the h(u)>0 for all u. Show that the u-parameter curves are all

geodesics

[Difficulty]

I'm revising for an exam and I don't know what to do!!

[Thoughts]

Ok first of all, should I be able to know how they got the coordinate

patch? Once I have it I know how to work with it but I don't know how

they got it!

I have loads of theory to work off, I'm just not sure how to apply it.

U-parameter curves can only be geodesic if unit speed so for starters

do I need to check that this is unit speed? Or make it unit speed?

Why is it only the u-parameter curves that will be geodesics?

A regular curve a(t) on a surface is a geodesic of the surface is

a''_tan=0

Looking at my notes I have the following formula

a''.(T X n) as the geodesic curvature. How is this, have the t's been

suppressed? Like is it a''(t).(T(t) X n(t))?

This doesn't really help me though does it? Since I don't have the

original curve except in terms of functions?

Sorry I'm really confused!