Super W-Symmetries, Covariantly Constant Forms And Duality Transformations

On a supersymmetric sigma model the covariantly constant forms are related to the conserved currents that are generators of a super W-algebra extending the superconformal algebra. The existence of covariantly constant forms restricts the holonomy group of the manifold. Via duality transformation we get new covariantly constant forms, thus restricting the holonomy group of the new manifold.