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On a new construction of special Lagrangian immersions in complex Euclidean space. (English) Zbl 1086.53074
The authors study special Lagrangian immersions into the $$n$$-dimensional complex space $${\mathbb C}^n$$ which are invariant with respect the standard action of $$\text{SO}(p+1) \times \text{SO}(q+1)$$ on $${\mathbb C}^n = {\mathbb C}^{p+1} \times {\mathbb C}^{q+1}$$, $$p+q+2=n$$. They construct explicit examples of such submanifolds and prove that, assuming that $$p,q \geq 2$$, any such an immersion is congruent to an open subset of one of their examples. In the case when $$p=1, q=0$$ their examples reduce to $$U(1)$$-invariant submanifolds studied by D. Joyce [Proc. Lond. Math. Soc., III. Ser. 85, No. 1, 233–256 (2002; Zbl 1023.53034)].

##### MSC:
 53C38 Calibrations and calibrated geometries
##### Keywords:
special Lagrangian submanifolds
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