Journal of Symplectic Geometry

Volume 17 (2019)

Number 5

A characterisation of toric locally conformally Kähler manifolds

Pages: 1297 – 1316



Nicolina Istrati (Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université Sorbonne Paris Cité, Paris, France)


We prove that a compact toric locally conformally Kähler manifold which is not Kähler admits a toric Vaisman structure. This is the final step leading to the classification of compact toric locally conformally Kähler manifolds. We also show, by constructing an example, that unlike in the symplectic case, toric locally conformally symplectic manifolds are not necessarily toric locally conformally Kähler.

Received 5 February 2017

Accepted 5 September 2018

Published 20 November 2019