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Lagrangian submanifolds in the homogeneous nearly Kähler S3×S3

Abstract : In this paper, we investigate Lagrangian submanifolds in the homogeneous nearly Kähler S3×S3. We introduce and make use of a triplet of angle functions to describe the geometry of a Lagrangian submanifold in S3×S3. We construct a new example of a flat Lagrangian torus and give a complete classification of all the Lagrangian immersions of spaces of constant sectional curvature. As a corollary of our main result, we obtain that the radius of a round Lagrangian sphere in the homogeneous nearly Kähler S3×S3 can only be 2/√3 or 4/√3.
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https://hal-uphf.archives-ouvertes.fr/hal-03148562
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Submitted on : Wednesday, July 13, 2022 - 11:28:19 AM
Last modification on : Wednesday, July 20, 2022 - 10:04:16 AM

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Bart Dioos, Luc Vrancken, Xianfeng Wang. Lagrangian submanifolds in the homogeneous nearly Kähler S3×S3. Annals of Global Analysis and Geometry, Springer Verlag, 2018, 53 (1), pp.39-66. ⟨10.1007/s10455-017-9567-z⟩. ⟨hal-03148562⟩

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