具有扭转指标的Strong Kähler变形

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2020-08-27 DOI:10.1515/coma-2020-0120

Riccardo Piovani, Tommaso Sferruzza

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引用次数: 4

摘要

摘要:证明了复杂流形上具有扭转度量(简称SKT度量)的强Kähler在小变形下是不稳定的。我们找到了沿复流形{Mt}t的可微族的厄密度量{ωt}t光滑曲线在t = 0时等于一个固定的SKT度量ω的性质是SKT稳定的必要条件。

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Deformations of Strong Kähler with torsion metrics

Abstract Existence of strong Kähler with torsion metrics, shortly SKT metrics, on complex manifolds has been shown to be unstable under small deformations. We find necessary conditions under which the property of being SKT is stable for a smooth curve of Hermitian metrics {ωt }t which equals a fixed SKT metric ω for t = 0, along a differentiable family of complex manifolds {Mt}t.

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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.