On Product Minimal Lagrangian Submanifolds in Complex Space Forms

Xiuxiu Cheng , Zejun Hu , Marilena Moruz , Luc Vrancken (1)

1 LMI - Laboratoire de Mathématiques pour l’Ingénieur

In this paper we consider minimal Lagrangian submanifolds in n-dimensional complex space forms. More precisely, we study such submanifolds which, endowed with the induced metrics, write as a Riemannian product of two Riemannian manifolds, each having constant sectional curvature. As the main result, we give a complete classification of these submanifolds.

Mots clés: Calabi product immersion; Complex space form; Minimal Lagrangian submanifold; Product submanifold

Domaines: Mathématiques [math]

Xiuxiu Cheng, Zejun Hu, Marilena Moruz, Luc Vrancken. On Product Minimal Lagrangian Submanifolds in Complex Space Forms. The Journal of Geometric Analysis, 2021, 31 (2), pp.1934-1964. ⟨10.1007/s12220-019-00328-7⟩. ⟨hal-03722540⟩