Author(s) :
Luc Vrancken
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 644-1999
MSC 2000
- 53B35 Hermitian and Kählerian structures
-
53B30 Lorentz metrics, indefinite metrics
Abstract :
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.
Keywords :
Lagrangian, constant sectional curvature, complex space forms