creat a datum plane that is parallel to the surface that you want to project the curve on to, if you don' already have one. then go to creat datum curve then pick projection. it will alsk for sketch plane, use the one you just created or one already there. sketch your curve, after out of sketch mode it will ask for surface to include the curve on. then all done.
I just see your problem and I want to add something something about projecting surfaces.
Follow the above instructions but have in mind this :
There is two ways to project a curve on a specified surface.
Formed and Projected
With formed curve command you project a curve on a surface and as result you have a projected curve that has the same dimensions (for example if you project a curve by formed command you can see that the projected has the same diameter as the parent curve)
With projected curve you can see that the parent curve follows the surface and as a result you have a child curve which is adaptive to the projected surface.