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arXiv · 1809.05304

Nearly K\"ahler six-manifolds with two-torus symmetry

Giovanni Russo·Andrew Swann
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Abstract

We consider nearly K\"ahler 6-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 K\"ahler six-manifolds from three-dimensional data. This is illustrated for structures on the Heisenberg group.

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Giovanni Russo, Andrew Swann. 2018-09-14. Nearly K\"ahler six-manifolds with two-torus symmetry. https://doi.org/10.1016/j.geomphys.2018.12.016

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