2019/11/27 by Giovanni Russo, Russo, Giovanni · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG
paper · pdf · doi:10.48550/arxiv.1911.12420
23 pages, 4 figures. Propositions 3.2, 4.2, 5.2 and Examples 6.2-6.3 added. General exposition improved and some minor mistakes fixed. This is a pre-print of an article published in Geometriae Dedicata. The final version is available at https://doi.org/10.1007/s10711-020-00568-w
arxiv created 2020/09/19 · arxiv updated 2020/09/22
We study multi-moment maps induced by a two-torus action on the four homogeneous nearly Kähler six-manifolds. Their explicit expression and stationary orbits are derived. The configuration of fixed-points and one-dimensional orbits is worked out for generic six-manifolds equipped with an SU(3)-structure admitting a two-torus symmetry. Projecting the subspaces obtained to the orbit space yields a trivalent graph. We illustrate this result concretely on the homogeneous nearly Kähler examples.