Lagrangian submanifolds in the homogeneous nearly Kähler S3×S3

Bart Dioos (1) , Luc Vrancken (1, 2, 3) , Xianfeng Wang (4)

1 KU Leuven - Catholic University of Leuven = Katholieke Universiteit Leuven
2 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
3 INSA Hauts-De-France - INSA Institut National des Sciences Appliquées Hauts-de-France
4 Nankai University. School of Mathematical Sciences and LPMC

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.

Mots clés: Nearly Kähler manifold; Lagrangian submanifolds; Constant sectional curvature; Lagrangian sphere; Lagrangian torus

Domaines: Mathématiques [math]

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⟩