Matsuo, Koji Pseudo-Bochner curvature tensor on Hermitian manifolds. (English) Zbl 0940.53039 Colloq. Math. 80, No. 2, 201-209 (1999). 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) Cited in 3 Documents MSC: 53C55 Global differential geometry of Hermitian and Kählerian manifolds Keywords:Hermitian manifold; curvature tensor; conformal invariant; constant holomorphic sectional curvature PDFBibTeX XMLCite \textit{K. Matsuo}, Colloq. Math. 80, No. 2, 201--209 (1999; Zbl 0940.53039) Full Text: DOI EuDML