  It is known that generalized deformation in the sense of Hitchin-Gaultieri is
a geometric realization of the degree-2 component of Kontsevich-Barannikov's
homological approach to extended deformation. Through extended deformation, one
associates a Frobenius structure to the extended moduli space. In this notes,
we prove that on primary Kodaira manifolds the restriction of the Frobenius
structure on the degree-2 component of the extended moduli space is trivial. It
generalizes the author's past observation on Kodaira surface.
