Totally geodesic Lagrangian submanifolds of the pseudo-nearly Kähler
$\text{SL}(2,\mathbb{R})\times\text{SL}(2,\mathbb{R})$
Mateo Anarella
KU Leuven/UPHF, Leuven, Belgium
Abstract:
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 $\widetilde{M}$.