The multi-moment maps of the nearly Kähler S3×S3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S^3\times S^3$$\end{document}

The homogeneous nearly Kähler structure on S3×S3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S^3\times S^3$$\end{document} is the only known complete 6-dimensional strictly nearly Kähler structure which is invariant under the action of a 3-torus. We investigate the multi-moment maps associated to such an action and compare with the usual moment map of a toric manifold.