Almost complex surfaces in the nearly Kaehler 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.