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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| Format: | article |
| Langue: | EN |
| Publié: |
De Gruyter
2020
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| Sujets: | |
| Accès en ligne: | https://doaj.org/article/4a554441c5234cc48432cc7fd70ff4fd |
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| Résumé: | 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. |
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