Generalized Frobenius manifolds with non-flat unity and bihamiltonian integrable hierarchies

We consider the relation between a class of generalized Frobenius manifolds with bihamiltonian integrable hierarchies. Such generalized Frobenius manifolds are defined by Dubrovin’s definition of Frobenius manifold but without the flatness condition imposed on the unit vector fields. Important examples arise from the study of Gromov–Witten theory and Hodge integrals. For any semisimple generalized Frobenius manifold, we present an analogue of the construction of bihamiltonian integrable hierarchies that was given by Dubrovin and Zhang for semisimple Frobenius manifolds.