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

Abstract

In this paper, we study Lagrangian submanifolds of the pseudo-nearly Kähler $\mathrm{SL}(2,\mathbb{R})\times \mathrm{SL}(2,\mathbb{R})$. 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.

23 pages, accepted for publication in Mathematische Nachrichten