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Nearly Kähler six-manifolds with two-torus symmetry

Andrew Swann and Giovanni Russo present new results on arXiv

2018.10.01 | Christine Dilling

Andrew Swann and his PhD student Giovanni Russo recently submitted a new result on arXiv.

In this paper they consider nearly Kähler 6-manifolds with effective 2-torus symmetry. The multi-moment map for the T2-action becomes an eigenfunction of the Laplace operator. At regular values, they prove the T2-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.   

Link to the paper on arXiv