SPECIAL LAGRANGIAN 4-FOLDS WITH SO(2)⋊S3-SYMMETRY IN COMPLEX SPACE FORMS

Abstract : In this article we obtain a classification of special Lagrangian submanifolds in complex space forms subject to a pointwise SO(2)⋊S3-symmetry on the second fundamental form. The algebraic structure of this form has been obtained by Marianty Ionel in [8]. However, the classification of special Lagrangian submanifolds in C4 having this SO(2)⋊S3 symmetry in [8] is incomplete. In this paper we give a complete classification of such submanifolds, and extend the classification to special Lagrangian submanifolds of arbitrary complex space forms with a pointwise SO(2)⋊S3-symmetry in the second fundamental form.