Cutting surface with curves in grasshopper

Hi, I need to cut a surface with a curve.
i projected the curve on the surface and i used split surface to trim it, but it doesn’t work!
I attach the file
please find an answer
trim surface problem.3dm (607.1 KB)
trim surface problem.gh (12.8 KB)

Your curve is not closed.
Close it.
You can use “Connect curves” with Close(L)=true.

wonderful
thank you very much