Almost complex surfaces in the nearly Kaehler flag manifold

TL;DR

This paper classifies almost complex totally geodesic submanifolds within the nearly Kaehler flag manifold and explores its structural properties, including curvature tensor expressions related to the nearly Kaehler structure.

Contribution

It provides a classification of certain submanifolds and develops a structural framework for understanding the nearly Kaehler flag manifold's geometry.

Findings

Classification of almost complex totally geodesic submanifolds

Expression of curvature tensor in terms of nearly Kaehler structure

Structural insights into the geometry of the flag manifold

Abstract

We study and classify almost complex totally geodesic submanifolds of the nearly Kaehler flag manifold $F_{1,2}(\mathbb C^3)$, and of its semi-Riemannian counterpart. We also develop a structural approach to the nearly Kaehler flag manifold $F_{1,2}(\mathbb C^3)$, expressing for example the curvature tensor in terms of the nearly Kaehler structure $J$ and the three canonical orthogonal complex structures.