Geometria Complessa e Geometria Differenziale
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G. Russo

Multi-moment maps on nearly Kähler six-manifolds

created by russo on 19 Feb 2020
modified on 05 Apr 2023


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

ArXiv: 1911.12420 PDF


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.

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