Nearly Kähler six-manifolds with two-torus symmetry

Giovanni Russo, Andrew Francis Swann

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Abstract

We consider nearly Kähler-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.

OriginalsprogEngelsk
TidsskriftJournal of Geometry and Physics
Vol/bind138
NummerApril
Sider (fra-til)144-153
Antal sider10
ISSN0393-0440
DOI
StatusUdgivet - 2019

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