On a new construction of special Lagrangian immersions in complex Euclidean space. (English) Zbl 1086.53074

Castro, Ildefonso; Urbano, Francisco

Q. J. Math. 55, No. 3, 253-265 (2004).

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)].

Reviewer: Iskander A. Taimanov (Novosibirsk)

MSC:

53C38

Calibrations and calibrated geometries

Keywords:

special Lagrangian submanifolds