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Lagrangian submanifolds of the nearly Kähler S3 × S3 from minimal surfaces in S3

Abstract : We study non-totally geodesic Lagrangian submanifolds of the nearly Kähler S3 × S3 for which the projection on the first component is nowhere of maximal rank. We show that this property can be expressed in terms of the so-called angle functions and that such Lagrangian submanifolds are closely related to minimal surfaces in S3. Indeed, starting from an arbitrary minimal surface, we can construct locally a large family of such Lagrangian immersions, including one exceptional example. We also show that locally all such Lagrangian submanifolds can be obtained in this way.
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https://hal-uphf.archives-ouvertes.fr/hal-03156192
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Submitted on : Tuesday, March 2, 2021 - 12:04:32 PM
Last modification on : Saturday, October 9, 2021 - 3:15:50 AM

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Marilena Moruz. Lagrangian submanifolds of the nearly Kähler S3 × S3 from minimal surfaces in S3. Colloque PADGE 2017, Aug 2017, Leuven, Belgium. pp.655-689, ⟨10.1017/prm.2018.43⟩. ⟨hal-03156192⟩

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