Almost complex totally geodesic surfaces in the nearly Kähler $\frac{\text{SL}(3,\mathbb{R})}{\mathbb{R}\times \text{SO}(2)}$

Abstract

We give a detailed description of the nearly Kähler $\frac{\mathrm{SL}(3,\mathbb{R})}{\mathbb{R}\times \mathrm{SO}(2)}$, which is one of the pseudo-Riemannian counterparts of the flag manifold $F({\mathbb{C}}^3)$. The main result is the classification of totally geodesic almost complex surfaces in this space.