Multi-moment maps on nearly K\"ahler six-manifolds

Giovanni Russo

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arXiv · 1911.12420

Multi-moment maps on nearly K\"ahler six-manifolds

Giovanni Russo

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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 $\mathrm{SU}(3)$-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 K\"ahler examples.

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Giovanni Russo. 2019-11-27. Multi-moment maps on nearly K\"ahler six-manifolds. https://arxiv.org/abs/1911.12420

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