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BY 4.0 license Open Access Published by De Gruyter Open Access April 3, 2020

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

  • Masaya Kawamura EMAIL logo
From the journal Complex 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 Bi¯j¯λBλji0, 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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Received: 2019-09-08
Accepted: 2020-03-13
Published Online: 2020-04-03

© 2020 Masaya Kawamura, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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