English

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

Differential Geometry 2026-01-07 v1

Abstract

We give a detailed description of the nearly K\"ahler SL(3,R)R×SO(2)\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(C3)F(\mathbb{C}^3). The main result is the classification of totally geodesic almost complex surfaces in this space.

Keywords

Cite

@article{arxiv.2601.02733,
  title  = {Almost complex totally geodesic surfaces in the nearly K\"ahler $\frac{\text{SL}(3,\mathbb R)}{\mathbb R\times \text{SO}(2)}$},
  author = {Mateo Anarella and Xiuxiu Cheng and Marie D'haene and Zejun Hu and Luc Vrancken},
  journal= {arXiv preprint arXiv:2601.02733},
  year   = {2026}
}