On Kähler-like and G-Kähler-like almost Hermitian manifolds

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2020-01-01 DOI:10.1515/coma-2020-0009

Masaya Kawamura

引用次数: 5

Abstract

Abstract We introduce Kähler-like, G-Kähler-like metrics on almost Hermitian manifolds. We prove that a compact Kähler-like and G-Kähler-like almost Hermitian manifold equipped with an almost balanced metric is Kähler. We also show that if a Kähler-like and G-Kähler-like almost Hermitian manifold satisfies B i¯j¯λBλji≥0 B_{\bar i\bar j}^\lambda B_{\lambda j}^i \ge 0 , then the metric is almost balanced and the almost complex structure is integrable, which means that the metric is balanced. We investigate a G-Kähler-like almost Hermitian manifold under some assumptions.

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在Kähler-like和G-Kähler-like上几乎是厄米流形

摘要引入了近似厄米流形上的Kähler-like、G-Kähler-like度量。我们证明了一个紧致的Kähler-like和G-Kähler-like几乎厄米流形具有一个几乎平衡度量是Kähler。我们还证明了如果一个Kähler-like和G-Kähler-like几乎厄米流形满足B i¯j¯λBλji≥0 B＿ {\bar i \bar j}^\lambda B＿ {\lambda j}^i\ge 0，则度量是几乎平衡的，并且几乎复杂的结构是可积的，这意味着度量是平衡的。我们研究了在某些假设下的G-Kähler-like概厄米流形。

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.