Published Paper
Inserted: 19 feb 2020
Last Updated: 5 apr 2023
Journal: Geometriae Dedicata
Volume: 213
Number: 1
Pages: 57-81
Year: 2021
Doi: 10.1007/s10711-020-00568-w
Abstract:
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 $\mathrm{SU}(3)$-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.