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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.
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Submitted on : Monday, February 22, 2021 - 11:20:38 AM
Last modification on : Tuesday, October 19, 2021 - 6:38:15 PM

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Franki Dillen, Christine Scharlach, Kristof Schoels, Luc Vrancken. SPECIAL LAGRANGIAN 4-FOLDS WITH SO(2)⋊S3-SYMMETRY IN COMPLEX SPACE FORMS. Taiwanese Journal of Mathematics, TJM, Mathematical Society of the Republic of China (Taiwan), 2015, 19 (3), pp.759-792. ⟨10.11650/tjm.19.2015.4951⟩. ⟨hal-03148413⟩

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