Locally conformally Kähler solvmanifolds: a survey

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2018-11-22 DOI:10.1515/coma-2019-0003

A. Andrada, M. Origlia

引用次数: 4

Abstract

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.

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局部共形Kähler溶剂流形：综述

摘要流形上的Hermitian结构称为局部保形Kähler（LCK），如果它局部允许保形变化，即Kächler。在这项调查中，我们回顾了溶剂流形上不变LCK结构的最新结果，并给出了关于配备有Vaisman结构的溶剂流形的正则丛的原始结果，即，其相关Lee形式是平行的LCK结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.