Gauging N=2 Supersymmetric Non-Linear $\sigma$-Models in the Atiyah-Ward   Space-Time
  We build up a class of N=2 supersymmetric non-linear $\sigma$-models in an N=1 superspace based on the Atiyah-Ward space-time of (2+2)-signature metric. We also discuss the gauging of isometries of the associated hyper-K\"ahlerian target spaces and present the resulting gauge-covariant supersymmetric action functional. 
M. Carvalho and M.W. de Oliveira