Summary
Concerning the integrability of almost Kähler manifolds, there is a longstanding conjecture by S.I. Goldberg, “A compact almost Kähler Einstein manifold is Kähler”. The conjecture is true in the case where the scalar curvature is non-negative. However, the conjecture is still open in the remaining case. In this note, we shall give a brief survey on the recent progress concerning the conjecture in four-dimensional case.
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Dedicated to Professor Lieven Vanhecke
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Oguro, T., Sekigawa, K. (2005). Notes on the Goldberg Conjecture in Dimension Four. In: Kowalski, O., Musso, E., Perrone, D. (eds) Complex, Contact and Symmetric Manifolds. Progress in Mathematics, vol 234. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4424-5_15
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