Minimal Lagrangian submanifolds with constant sectional curvature in indefinite complex space

We study minimal Lagrangian immersions from an indefinite real space form M-s(n) (c) into an indefinite complex space form (M) over tilde (n)(s) (4 (c) over tilde). Provided that c not equal (c) over tilde, we show that M-s(n) (c) has to be at and we obtain an explicit description of the immersion. In the case when the metric is positive definite or Lorentzian, this result was respectively obtained by Ejiri (1982) and by Kriele and the author (1999). In the case that c = (c) over tilde, this theorem is no longer true; see for instance the examples discovered by Chen and the author (accepted for publication in the Tohoku Mathematical Journal).