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like a barrel cam?
create a couple of planes at angles through the axis of the cylinder, draw a line representing half of the section of the top, then loft together using tangency end conditions, and pattern the result around.
you can do this with solids or surfaces.
you could also just draw directly on the face of the cylinder with the spline on surface tool, all depends on how accurate you need to be and what type of data you are working from.
When you said you're "trying to create a curve on the edge of a surface" is that edge already existing? If so just click 3D sketch and use the convert entities Sketch tool.
If you're trying to create a curve on a cylinder but with a newly created curve, use the Spline on surface command to create your wavy curve around the cylinder. Check out this tread for similar example