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On Kähler-like and G-Kähler-like almost Hermitian manifolds
2020
Complex Manifolds
AbstractWe 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_{\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
doi:10.1515/coma-2020-0009
fatcat:kkq6h7cjbfg2jae2irkhbfgclq