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Lagrangian submanifolds in the homogeneous nearly Kähler S3×S3

Bart Dioos 1 Luc Vrancken 1, 2 Xianfeng Wang 3
1 KU Leuven - Catholic University of Leuven - Katholieke Universiteit Leuven
2 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
3 Nankai University. School of Mathematical Sciences and LPMC
Nankai University, School of mathematical sciences
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.
Keywords : Nearly Kähler manifold Lagrangian submanifolds Constant sectional curvature Lagrangian sphere Lagrangian torus
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Submitted on : Monday, February 22, 2021 - 12:39:22 PM
Last modification on : Tuesday, October 19, 2021 - 6:38:17 PM

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UNIV-VALENCIENNES | INSMI | CNRS | LAMAV

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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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