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

preprint2026arXivOpen access

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.

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

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

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