Locally conformally Kähler solvmanifolds: A survey

A. Andrada; M. Origlia

doi:10.1515/coma-2019-0003

Locally conformally Kähler solvmanifolds: A survey

A. Andrada, M. Origlia

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

3 Citations (Scopus)

Abstract

A Hermitian structure on a manifold is called locally conformally Kähler (LCK) if it locally admits a conformal change which is Kähler. In this survey we review recent results of invariant LCK structures on solvmanifolds and present original results regarding the canonical bundle of solvmanifolds equipped with a Vaisman structure, that is, a LCK structure whose associated Lee form is parallel.

Original language	English
Pages (from-to)	65-87
Number of pages	23
Journal	Complex Manifolds
Volume	6
Issue number	1
DOIs	https://doi.org/10.1515/coma-2019-0003
Publication status	Published - Jan 2019
Externally published	Yes

Keywords

Locally conformally Kähler manifold, solvable Lie group, solvmanifold.

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abstract = "A Hermitian structure on a manifold is called locally conformally K{\"a}hler (LCK) if it locally admits a conformal change which is K{\"a}hler. In this survey we review recent results of invariant LCK structures on solvmanifolds and present original results regarding the canonical bundle of solvmanifolds equipped with a Vaisman structure, that is, a LCK structure whose associated Lee form is parallel.",

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AU - Origlia, M.

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AB - A Hermitian structure on a manifold is called locally conformally Kähler (LCK) if it locally admits a conformal change which is Kähler. In this survey we review recent results of invariant LCK structures on solvmanifolds and present original results regarding the canonical bundle of solvmanifolds equipped with a Vaisman structure, that is, a LCK structure whose associated Lee form is parallel.

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Locally conformally Kähler solvmanifolds: A survey

Abstract

Keywords

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