Geometry of N=4 Twisted String

We compare N=2 string and N=4 topological string within the framework of the sigma model approach. Being classically equivalent on a flat background, the theories are shown to lead to different geometries when put in a curved space. In contrast to the well studied Kähler geometry characterising the former case, in the latter case a manifold has to admit a covariantly constant holomorphic two--form in order to support an N=4 twisted supersymmetry.This restricts the holonomy group to be a subgroup of SU(1,1) and leads to a Ricci--flat manifold. We speculate that, the N=4 topological formalism is an appropriate framework to smooth down ultraviolet divergences intrinsic to the N=2 theory.