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Conference Papers Year : 2019

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

Marilena Moruz
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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-03156192 , version 1 (05-07-2022)

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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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