2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70297This work continues the study of $F$--manifolds $(M,\circ)$, first defined by Hertling and Manin and investigated in [He]. The notion of a compatible flat structure $\nabla$ is introduced, and it is shown that many constructions known for Frobenius manifolds do not in fact require invariant metrics and can be developed for all such triples $(M,\circ ,\nabla).$ In particular, we extend and generalize recent Dubrovin's duality.22 pagesDifferential GeometryAlgebraic Geometry14H10text