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

Abstract

We give a detailed description of the nearly K\"ahler $\frac{\mathrm{SL}(3,\mathbb R)}{\mathbb R\times \mathrm{SO}(2)}$, 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.