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Journal Articles Annals of Global Analysis and Geometry Year : 2018

Lagrangian submanifolds in the homogeneous nearly Kähler S3×S3

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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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Dates and versions

hal-03148562 , version 1 (13-07-2022)

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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, 2018, 53 (1), pp.39-66. ⟨10.1007/s10455-017-9567-z⟩. ⟨hal-03148562⟩
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