Totally geodesic Lagrangian submanifolds of the pseudo-nearly Kähler SL(2,ℝ)\timesSL(2,ℝ)

2023/07/25 by Mateo Anarella, Anarella, Mateo, Joeri Van der Veken +1
Mathematics · Physics and Astronomy · #53C42 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2307.13389

openalex publication_date 2023/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study Lagrangian submanifolds of the pseudo-nearly Kähler SL(2,ℝ)\timesSL(2,ℝ). First, we show that they split into four different classes depending on their behaviour with respect to a certain almost product structure on the ambient space. Then, we give a complete classification of totally geodesic Lagrangian submanifolds of this space.

Related

• Extrinsically homogeneous Lagrangian submanifolds of the pseudo-nearly Kähler SL(2,ℝ)\timesSL(2,ℝ)
• Lagrangian submanifolds of the nearly Kähler full flag manifold F_1,2(ℂ³)
• Almost complex surfaces in the nearly Kahler SL(2,R)xSL(2,R)
• Lagrangian submanifolds of the nearly Kähler \mathbbS³ × \mathbbS³ from minimal surfaces in \mathbbS³
• Lagrangian submanifolds in the nearly kaehler s³ × s³