Totally geodesic Lagrangian submanifolds of the pseudo‐nearly Kähler SL(2,R)×SL(2,R)SL(2,R)× SL(2,R)

In this paper, we study Lagrangian submanifolds of the pseudo‐nearly Kähler . First, we show that they split into four different classes depending on their behavior 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.