Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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G. Russo - A. Swann

Nearly Kähler six-manifolds with two-torus symmetry

created by russo on 19 Feb 2020
modified on 27 Apr 2021


Published Paper

Inserted: 19 feb 2020
Last Updated: 27 apr 2021

Journal: Journal of Geometry and Physics
Volume: 138
Pages: 144-153
Year: 2019
Doi: 10.1016/j.geomphys.2018.12.016

ArXiv: 1809.05304 PDF
Links: Link to the journal


We consider nearly Kähler 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 Kähler six-manifolds from three-dimensional data. This is illustrated for structures on the Heisenberg group.

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