Differential operators on almost-Hermitian manifolds and harmonic forms

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2019-09-14 DOI:10.1515/coma-2020-0006

Nicoletta Tardini, A. Tomassini

引用次数: 18

Abstract

Abstract We consider several differential operators on compact almost-complex, almost-Hermitian and almost-Kähler manifolds. We discuss Hodge Theory for these operators and a possible cohomological interpretation. We compare the associated spaces of harmonic forms and cohomologies with the classical de Rham, Dolbeault, Bott-Chern and Aeppli cohomologies.

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几乎厄米流形和调和形式上的微分算子

研究紧致几乎复流形、几乎厄米流形和almost-Kähler流形上的几种微分算子。我们讨论了这些算子的Hodge理论和一种可能的上同解释。我们将调和形式和上同调的关联空间与经典的de Rham, Dolbeault, bot - chern和Aeppli上同调进行了比较。

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.