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

Vrancken, Luc

Inst. Mathematik

We study minimal Lagrangian immersions from an indefinite real space form $M^n_s(c)$ into an indefinite complex space form $\tilde{M}^n_s(4\tilde{c})$. Provided that $c\not= \tilde{c}$, we show that $M^n$ has to be flat and we obtain an explicit description of the immersion. In the case the metric is positive definite or Lorentzian, this result was respectively obtained by Ejiri [4] and by Kriele and the author [5]. In the case that $c = \tilde{c}$, this theorem is no longer true, see for instance the examples discovered in [3] by Chen and the author.