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Pseudo-Bochner curvature tensor on Hermitian manifolds. (English) Zbl 0940.53039

The author introduces, on a Hermitian manifold \(M\), a pseudo-curvature tensor \(P\) and a pseudo-Bochner curvature tensor \(B_H\). He proves that \(B_H\) is conformally invariant and obtains a condition for \(M\) to have pointwise constant holomorphic sectional curvature in terms of \(P\). He also shows that if \(M\) has pointwise constant holomorphic sectional curvature, then \(B_H=0\).
Reviewer: K.Ogiue (Tokyo)

MSC:

53C55 Global differential geometry of Hermitian and Kählerian manifolds
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