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Lagrangian submanifolds in the homogeneous nearly Kahler S3×S3 with constant sectional curvature

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-03155933
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Submitted on : Tuesday, March 2, 2021 - 10:33:57 AM
Last modification on : Tuesday, October 19, 2021 - 3:07:25 PM

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  • HAL Id : hal-03155933, version 1

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Luc Vrancken. Lagrangian submanifolds in the homogeneous nearly Kahler S3×S3 with constant sectional curvature. XIX Geometrical Seminar, Aug 2016, Zlatibor, Serbia. ⟨hal-03155933⟩

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