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Minimal Lagrangian submanifolds with constant sectional curvature in indefinite complex space forms. (English) Zbl 0999.53052
The author studies minimal Lagrangian immersions from an indefinite real space form M s n (c) into an indefinite complex space form M ¯ s n (4c ¯), c ¯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 N. Ejiri [Proc. Am . Math. Soc. 84, 243-246 (1982; Zbl 0485.53022)] and by M. Kriele and L. Vrancken [Arch. Math. 72, 223-232 (1999; Zbl 0969.53045)].
MSC:
53D12Lagrangian submanifolds; Maslov index
53B25Local submanifolds
53B30Lorentz metrics, indefinite metrics
53C50Lorentz manifolds, manifolds with indefinite metrics