Biflat F-structures as differential bicomplexes and Gauss–Manin connections

We show that a biflat F-structure (Formula presented.) on a manifold (Formula presented.) defines a differential bicomplex (Formula presented.) on forms with value on the tangent sheaf of the manifold. Moreover, the sequence of vector fields defined recursively by (Formula presented.) coincides with the coefficients of the formal expansion of the flat local sections of a family of flat connections (Formula presented.) associated with the biflat structure. In the case of Dubrovin–Frobenius manifold, the connection (Formula presented.) (for suitable choice of an auxiliary parameter) can be identified with the Levi–Civita connection of the flat pencil of metrics defined by the invariant metric and the intersection form.