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

TL;DR

This paper classifies almost complex totally geodesic surfaces within the nearly Kähler space formed by the quotient of SL(3,R), providing insights into its geometric structure and pseudo-Riemannian properties.

Contribution

It offers a detailed description and classification of totally geodesic almost complex surfaces in the nearly Kähler SL(3,R)/R×SO(2), a pseudo-Riemannian analog of the flag manifold.

Findings

Classification of totally geodesic almost complex surfaces achieved

Detailed geometric description of the nearly Kähler space provided

Insights into pseudo-Riemannian geometry of the space obtained

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.