Multi-moment maps on nearly K\"ahler six-manifolds
Abstract
We study multi-moment maps induced by a two-torus action on the four homogeneous nearly K\"ahler 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 -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 K\"ahler examples.
Cite
@article{arxiv.1911.12420,
title = {Multi-moment maps on nearly K\"ahler six-manifolds},
author = {Giovanni Russo},
journal= {arXiv preprint arXiv:1911.12420},
year = {2020}
}
Comments
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