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

Mateo Anarella; Xiuxiu Cheng; Marie D'haene; Zejun Hu; Luc Vrancken

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arXiv · 2601.02733

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

Mateo Anarella·Xiuxiu Cheng·Marie D'haene·Zejun Hu·Luc Vrancken

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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.

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Mateo Anarella, Xiuxiu Cheng, Marie D'haene, Zejun Hu, Luc Vrancken. 2026-01-06. Almost complex totally geodesic surfaces in the nearly K\"ahler $\frac{\text{SL}(3,\mathbb R)}{\mathbb R\times \text{SO}(2)}$. https://arxiv.org/abs/2601.02733

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