  The article gives a necessary and sufficient condition for a Frobenius
manifold to be a CDV-structure. We show that there exists a positive definite
CDV-structure on any semi-simple Frobenius manifold. We also compare three
natural connections on a CDV-structure and conclude that the underlying
Hermitian manifold of a non-trivial CDV-structure is not a Kahler manifold.
Finally, we compute the harmonic potential of a harmonic Frobenius manifolds.
