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

Luc Vrancken (1, 2, 3)

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

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]

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