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Journal Articles Proceedings of the Royal Society of Edinburgh: Section A, Mathematics Year : 2019

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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Dates and versions

hal-03156184 , version 2 (05-07-2022)
hal-03156184 , version 1 (05-07-2022)

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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, 2019, 149 (03), pp.655-689. ⟨10.1017/prm.2018.43⟩. ⟨hal-03156184v2⟩
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