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Four-dimensional almost Kähler Einstein manifolds. (English) Zbl 0731.53026
Let (M,J,g) be an almost Kähler manifold. The *-Ricci tensor is defined to be the trace of the map \(Z\to R(X,JZ)JY\), where R denotes the curvature tensor of M. M is said to be *-Einstein if the *-Ricci tensor is proportional to g. The authors prove that a 4-dimensional compact almost Kähler manifold which is Einstein and *-Einstein must be Kähler.
Reviewer: K.Ogiue (Tokyo)

MSC:
53B35 Local differential geometry of Hermitian and Kählerian structures
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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