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

2024/03/18 by Mateo Anarella, Anarella, Mateo
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.2403.11962

openalex publication_date 2024/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the pseudo-nearly Kähler SL(2,ℝ)\timesSL(2,ℝ) and we study its Lagrangian submanifolds. We provide examples of Lagrangian submanifolds which do not have an analogue in \mathbbS³×\mathbbS³. We also provide an expression for the isometry group of SL(2,ℝ)\timesSL(2,ℝ) with the pseudo-Riemannian nearly Kähler metric. The main result is a complete classification of extrinsically homogeneous Lagrangian submanifolds in this space.

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