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

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...

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Auteur principal:	Kawamura Masaya
Format:	article
Langue:	EN
Publié:	De Gruyter 2020
Sujets:	almost hermitian manifolds kähler-like metrics g-kähler-like metrics chern connection 53c15 (primary) 53c55 (secondary) Mathematics QA1-939
Accès en ligne:	https://doaj.org/article/4a554441c5234cc48432cc7fd70ff4fd
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id	oai:doaj.org-article:4a554441c5234cc48432cc7fd70ff4fd
record_format	dspace
spelling	oai:doaj.org-article:4a554441c5234cc48432cc7fd70ff4fd2021-12-02T17:14:47ZOn Kähler-like and G-Kähler-like almost Hermitian manifolds2300-744310.1515/coma-2020-0009https://doaj.org/article/4a554441c5234cc48432cc7fd70ff4fd2020-04-01T00:00:00Zhttps://doi.org/10.1515/coma-2020-0009https://doaj.org/toc/2300-7443We 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 Bi¯j¯λBλji≥0B_{\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.Kawamura MasayaDe Gruyterarticlealmost hermitian manifoldskähler-like metricsg-kähler-like metricschern connection53c15 (primary)53c55 (secondary)MathematicsQA1-939ENComplex Manifolds, Vol 7, Iss 1, Pp 145-161 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	almost hermitian manifolds kähler-like metrics g-kähler-like metrics chern connection 53c15 (primary) 53c55 (secondary) Mathematics QA1-939
spellingShingle	almost hermitian manifolds kähler-like metrics g-kähler-like metrics chern connection 53c15 (primary) 53c55 (secondary) Mathematics QA1-939 Kawamura Masaya On Kähler-like and G-Kähler-like almost Hermitian manifolds
description	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 Bi¯j¯λBλji≥0B_{\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.
format	article
author	Kawamura Masaya
author_facet	Kawamura Masaya
author_sort	Kawamura Masaya
title	On Kähler-like and G-Kähler-like almost Hermitian manifolds
title_short	On Kähler-like and G-Kähler-like almost Hermitian manifolds
title_full	On Kähler-like and G-Kähler-like almost Hermitian manifolds
title_fullStr	On Kähler-like and G-Kähler-like almost Hermitian manifolds
title_full_unstemmed	On Kähler-like and G-Kähler-like almost Hermitian manifolds
title_sort	on kähler-like and g-kähler-like almost hermitian manifolds
publisher	De Gruyter
publishDate	2020
url	https://doaj.org/article/4a554441c5234cc48432cc7fd70ff4fd
work_keys_str_mv	AT kawamuramasaya onkahlerlikeandgkahlerlikealmosthermitianmanifolds
_version_	1718381257544433664

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

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