Scalar tensor duality and N = 1,2 non-linear σ-models

Using N = 1 superfields, we investigate the duality between chiral multiplets and tensor multiplets. We find that the relation can be expressed in terms of a Legendre transform. We use this relation to construct new N = 2 non-linear σ-models corresponding to new Einstein-Kähler manifolds. We prove a no-go theorem for the N = 2 hypermultiplet and give off-shell formulations of the existing non-linear σ-models in terms of tensor multiplets.