On a supersymmetric sigma model the covariantly constant forms are rel
ated to the conserved currents that are generators of a super W-algebr
a extending the superconformal algebra. The existence of covariantly c
onstant forms restricts the holonomy group of the manifold. Via dualit
y transformation we get new covariantly constant forms, thus restricti
ng the holonomy group of the new manifold.