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

Mateo Anarella; Xiuxiu Cheng; Marie D’haene; Zejun HU; Luc Vrancken

doi:10.48550/arxiv.2601.02733

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

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Mateo Anarella, Xiuxiu Cheng, Marie D’haene, Zejun HU, Luc Vrancken

DOI: 10.48550/arxiv.2601.02733

Cited by: 0

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.

Fields of Study & Subjects

Geometry and complex manifolds Geometric Analysis and Curvature Flows Advanced Differential Geometry Research

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 6 January 2026
Document type: Preprint