Summary
We prove that a four-dimensional compact almost Kähler manifold which is Einsteinian, and Einsteinian is a Kähler manifold.
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Sekigawa, K., Vanhecke, L. Four-dimensional almost Kähler Einstein manifolds. Annali di Matematica pura ed applicata 157, 149–160 (1990). https://doi.org/10.1007/BF01765316
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DOI: https://doi.org/10.1007/BF01765316