Abstract
We show that along the almost Hermitian curvature flow, the non-positivity of the first Chern–Ricci curvature can be preserved if the initial almost Hermitian metric has the Griffiths non-positive Chern curvature. If additionally, the first Chern–Ricci curvature of the initial metric is negative at some point, then we show that the almost complex structure of a compact non-quasi-Kähler almost Hermitian manifold equipped with such a metric cannot be integrable.
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This study was funded by JSPS KAKENHI (grant number JP19K14543).
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This work was supported by JSPS KAKENHI Grant Number JP19K14543.
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Kawamura, M. Compact Almost Hermitian Manifolds with Quasi-negative Curvature and the Almost Hermitian Curvature Flow. Results Math 77, 162 (2022). https://doi.org/10.1007/s00025-022-01662-z
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DOI: https://doi.org/10.1007/s00025-022-01662-z