A characterisation of toric LCK manifolds
Differential Geometry
2017-01-13 v2
Abstract
We prove that a compact toric locally conformally K\"ahler manifold which is not K\"ahler admits a toric Vaisman structure, a fact which was conjectured in \cite{mmp}. This is the final step leading to the classification of compact toric locally conformally K\"ahler manifolds started in \cite{p} and \cite{mmp}. We also show, by constructing an example, that unlike in the symplectic case, toric locally conformally symplectic manifolds are not necessarily toric locally conformally K\"ahler.
Keywords
Cite
@article{arxiv.1612.03832,
title = {A characterisation of toric LCK manifolds},
author = {Nicolina Istrati},
journal= {arXiv preprint arXiv:1612.03832},
year = {2017}
}
Comments
14 pages. Example 6.4 added showing that the class of toric LCS manifolds strictly contains that of toric LCK manifolds. Some other minor changes