Almost Complex Surfaces in the Nearly Kähler Flag Manifold

We study and classify almost complex totally geodesic submanifolds of the nearly Kähler flag manifold F1,2(C3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_{1,2}(\mathbb C^3)$$\end{document}, and of its semi-Riemannian counterpart. We also develop a structural approach to the nearly Kähler flag manifold F1,2(C3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_{1,2}(\mathbb C^3)$$\end{document}, expressing for example the curvature tensor in terms of the nearly Kähler structure J and the three canonical orthogonal complex structures.