  A non-linear generalization of the Dirac operator in 4-dimensions, obtained
by replacing the spinor representation with a hyperKahler manifold admitting
certain symmetries, is considered. We show that the existence of a covariantly
constant, generalized spinor defines a Kahler structure on the base
4-dimensional manifold. For a class of hyperKahler manifolds obtained via
hyperKahler reduction, we also show that a harmonic spinor, under mild
conditions, defines a symplectic structure. Finally, we show that if a
covariantly constant, generalized spinor satisfies generalized Seiberg-Witten
equations, the metric on the base manifold has a constant scalar curvature.
