The geometry of sigma models with twisted supersymmetry

We investigate the relation between supersymmetry and geometry for two-dimensional sigma models with target spaces of arbitrary signature, and Lorentzian or Euclidean world-sheets. In . particular, we consider twisted forms of the two-dimensional p, q supersymmetry algebra. . Superspace formulations of the p, q heterotic sigma models with twisted or untwisted supersym- . metry are given. For the twisted 2,1 and the pseudo-Kahler sigma models, we give extended ¨