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arXiv · 1107.0855

Special Lagrangian 4-folds with $SO(2)\rtimes S_3$-Symmetry in Complex Space Forms

Franki Dillen·Christine Scharlach·Kristof Schoels·Luc Vrancken
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Abstract

In this article we obtain a classification of special Lagrangian submanifolds in complex space forms subject to an $SO(2)\rtimes S_3$-symmetry on the second fundamental form. The algebraic structure of this form has been obtained by Marianty Ionel. However, the classification of special Lagrangian submanifolds in $\mathbb{C}^4$ having this $SO(2)\rtimes S_3$ symmetry in that paper is incomplete. In the present paper we give a complete classification of such submanifolds, and extend the classification to special Lagrangian submanifolds of arbitrary complex space forms with $SO(2)\rtimes S_3$-symmetry.

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Franki Dillen, Christine Scharlach, Kristof Schoels, Luc Vrancken. 2011-07-05. Special Lagrangian 4-folds with $SO(2)\rtimes S_3$-Symmetry in Complex Space Forms. https://arxiv.org/abs/1107.0855

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