The Geometry of N=1 and N=2 Real Supersymmetric Non-Linear Sigma-Models   in the Atiyah-Ward Space-Time
  We analyse the structure of N=1 and N=2 supersymmetric non-linear sigma-models built up with a pair of real superfields defined in the superspace of Atiyah-Ward space-time. The geometry arising has new features such as the existence of a locally product structure (N=1 case) and a set of automorphisms of the tangent space that is isomorphic to the split-quaternionic algebra (N=2 case). 
M. Carvalho (1), J. A. Helayel-Neto (2), M. W. de Oliveira (2) ((1)   Dep. Mathematics Waseda University, (2) Centro Brasile...