Mateo Anarella
KU Leuven/UPHF, Leuven, Belgium

In this talk we will analyze the nearly Kähler structure of the pseudo-Riemannian manifold $\widetilde{M}=\text{SL}(2,\mathbb{R})\times\text{SL}(2,\mathbb{R})$. We can define a natural almost product structure $P$, compatible with the nearly Kähler metric, by swapping the vector fields tangent to each component of $\widetilde{M}$. Given a Lagrangian submanifold $M$, we will study the different forms the restriction $P|_{TM}$ can take. We classify, up to isometries, all totally geodesic Lagrangian submanifolds of $\widetilde{M}$.