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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-03156184
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Submitted on : Tuesday, March 2, 2021 - 12:00:04 PM
Last modification on : Saturday, October 9, 2021 - 3:15:44 AM

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Burcu Bektaş, Marilena Moruz, Joeri van der Veken, Luc Vrancken. Lagrangian submanifolds of the nearly Kähler S3 × S3 from minimal surfaces in S3. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Cambridge University Press (CUP), 2019, 149 (03), pp.655-689. ⟨10.1017/prm.2018.43⟩. ⟨hal-03156184⟩

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