In this talk, I will explain how to construct formal flat F-manifold structures on the primitive cohomology H of a Calabi-Yau smooth projective complete intersection variety X. My strategy is to convert an analysis on H to study on non-isolated hypersurface singularities using the Cayley trick\DSEMIC we associate a dGBV (differential Gerstenhaber-Batalin-Vilkovisky) algebra A to H, and find a special solution to Maurer-Cartan equation in order to construct formal flat F-manifolds.