  The aim of this talk is to derive two constraints imposed by supersymmetry
for a class of heterotic Landau-Ginzburg models with nonholomorphic
superpotentials. One of these constraints relates the nonholomorphic parameters
of the superpotential to the Hermitian curvature. Various special cases of this
constraint have been used to establish properties of Mathai-Quillen form
analogues which arise in the corresponding heterotic Landau-Ginzburg models.
The other constraint was not anticipated from studies of Mathai-Quillen form
analogues.
