Nearly Kähler six-manifolds with two-torus symmetry

Giovanni Russo, Andrew Francis Swann

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Abstract

We consider nearly Kähler six-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.
Original languageEnglish
JournalJournal of Geometry and Physics
Volume138
IssueApril
Pages (from-to)144-153
Number of pages10
ISSN0393-0440
DOIs
Publication statusPublished - 2019

Keywords

  • Nearly Kähler
  • Multi-moment map
  • Toric manifold

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