Let FΘ=U/KΘ\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {F}}_{\Theta }=U/K_\Theta $$\end{document} be a partial flag manifold, where KΘ\documentclass[12pt]{minimal}
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\begin{document}$$K_\Theta $$\end{document} is the centralizer of a torus in U. We study U-invariant almost Hermitian structures on FΘ\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {F}}_{\Theta }$$\end{document}. The classification of these structures are naturally related with the system Rt\documentclass[12pt]{minimal}
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\begin{document}$$R_{\mathfrak {t}}$$\end{document} of t\documentclass[12pt]{minimal}
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\begin{document}$${\mathfrak {t}}$$\end{document}-roots associated to FΘ\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {F}}_{\Theta }$$\end{document}. We introduced the notion of connectedness by triples with zero sum in a general subset of a vector space and proved that the set of t\documentclass[12pt]{minimal}
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\begin{document}$${\mathfrak {t}}$$\end{document}-roots satisfies this property. Using this result, the invariant G1\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {G}}_1$$\end{document} structures on FΘ\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {F}}_{\Theta }$$\end{document} are completely classified.
