A characterisation of toric locally conformally kähler manifolds

Nicolina Istrati

doi:10.4310/JSG.2019.v17.n5.a2

A characterisation of toric locally conformally kähler manifolds

Nicolina Istrati^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1297-1316
Number of pages	20
Journal	Journal of Symplectic Geometry
Volume	17
Issue number	5
DOIs	https://doi.org/10.4310/JSG.2019.v17.n5.a2
State	Published - 2019
Externally published	Yes

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10.4310/JSG.2019.v17.n5.a2

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abstract = "We prove that a compact toric locally conformally K{\"a}hler manifold which is not K{\"a}hler admits a toric Vaisman structure. This is the final step leading to the classification of compact toric locally conformally K{\"a}hler 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 K{\"a}hler.",

author = "Nicolina Istrati",

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A characterisation of toric locally conformally kähler manifolds

Abstract

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