# Institut for Matematik

## Nearly Kähler six-manifolds with two-torus symmetry

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### DOI

We consider nearly Kähler six-manifolds with effective 2-torus symmetry. The multi-moment map for the $T^2$-action becomes an eigenfunction of the Laplace operator. At regular values, we prove the $T^2$-action is necessarily free on the level sets and determines the geometry of three-dimensional quotients. An inverse construction is given locally producing nearly Kähler six-manifolds from three-dimensional data. This is illustrated for structures on the Heisenberg group.
Originalsprog Engelsk Journal of Geometry and Physics 138 April 144-153 10 0393-0440 https://doi.org/10.1016/j.geomphys.2018.12.016 Udgivet - 2019

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ID: 142408495