Nearly Kähler six-manifolds with two-torus symmetry

DOI10.1016/J.GEOMPHYS.2018.12.016zbMATH Open1414.53023arXiv1809.05304OpenAlexW2891133486MaRDI QIDQ2416870

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Publication date: 24 May 2019

Published in: (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1809.05304

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