Hi Leonard, there were some issues with the edges you showed in the pic as well as the ones crossing the seam of the top and bottom surfaces. I merged the edges and rebuilt them with the Rebuild command, then deleted the side surfaces and swept them back using the reconstructed edges.

When you need to project curves onto a surface like that it's always best drawing a sphere and cut it with a line, just as Pilou shows in his msg. This way you can leave out the seam, that often causes problems with fillet and offset.

Hope this helps,
cheers
Dan