Minimal Lagrangian submanifolds with constant sectional curvature in indefinite complex space forms (Q2781306)

The author studies minimal Lagrangian immersions from an indefinite real space form \(M_s^n(c)\) into an indefinite complex space form \(\overline{M}_s^n (4\overline{c})\), \(\overline{c}\neq c\), and obtains a complete classification. Amongst others it is proved that \(M_s^n(c)\) has to be flat. Therefore the author presents two classes of indefinite flat Lagrangian immersions. In the case when the metric is positive definite or Lorentzian, analogues results were respectively obtained by \textit{N. Ejiri} [Proc. Am . Math. Soc. 84, 243-246 (1982; Zbl 0485.53022)] and by \textit{M. Kriele} and \textit{L. Vrancken} [Arch. Math. 72, 223-232 (1999; Zbl 0969.53045)].