How can I project a geometry on a curved surface and carve it out from that surface?
First - Create a plane off that surface
Second - Make a Sketch that you want to be projected
Final - Do a Cut-Extrude, and make your start condition Surface/Face/Plane, and select the surface to where you want your projected sketch to be on. then you can enter the depth of the cut, or you can make it go up to next suface.