Update: the issue isn't the shape but that the first uses a spline and the second one uses lines. It seems you can only offset curves (splines)
When I do a more complex shape like this then I get a seam after revolving it
But when I do this simple shape I do not get a seam. Why is that and how can I fix it?
I need the seam to make an offset of the shape later on
An export of the last sketch is attached
The difference is in the complexity of the geometry. Your "no seam" case is made up of simple geometries (one cylinder, 2 tori, 2 planes, while the "seam" case is a more complex spline surface. Closed, periodic, spline surfaces will always have an edge in them, it is just the underlying math. You cannot get rid of this edge. You can hide it, by turning off visible edges. Why do you think you need to get rid of it? What problems is it causing? The surface should be continuous.
Sorry, @autodeskN884Q - I think I got that backwards - I assumed you wanted to get rid of the edge in the top case (because that is a common question here). If you want the edge in the lower case, you can use Split Face, but again, I'm interested in why you want that edge.
here is a screencast showing how to use Split Face to add in an edge, if you want one.
I would strongly discourage you from offsetting a projected curve! There are likely much more robust techniques for what you are trying to achieve. If you can share more details about what you are trying to achieve we can look into it.
