New examples of compact special lagrangian submanifolds embedded in hyper-Kähler manifolds

We construct smooth families of compact special Lagrangian submanifolds embedded in some toric hyper-Kähler manifolds, which never become holomorphic Lagrangian submanifolds via any hyper-Kähler rotations. These families converge to special Lagrangian immersions with self-intersection points in the sense of currents. To construct them, we apply the desingularization method developed by Joyce.

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Received 23 August 2016

Accepted 11 July 2018

Published 26 July 2019