Totally geodesic Lagrangian submanifolds of the pseudo-nearly K\'ahler $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$

Autor: Anarella, Mateo, Van der Veken, Joeri
Rok vydání: 2023
Předmět:
Druh dokumentu: Working Paper
Popis: In this paper, we study Lagrangian submanifolds of the pseudo-nearly K\"ahler $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$. 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.
Comment: 23 pages, accepted for publication in Mathematische Nachrichten
Databáze: arXiv