Kupeli, Demir N. On holomorphic and anti-holomorphic sectional curvature of indefinite Kähler manifolds of real dimension \(n\geq 6\). (English) Zbl 0804.53090 Manuscr. Math. 80, No. 1, 1-12 (1993). The author studies sufficient conditions to have a Kähler manifold \(M\) of (real) \(\dim M\geq 6\) with indefinite metric and constant holomorphic sectional curvature. These conditions are expressed in terms of bounded curvatures of holomorphic planes with signature \((-,-)\) (or \((+,+)\)) in \((\text{span}\{z,Jz\})^ \perp\), for each space-like vector \(z\in T_ p M\), provided that \(n-\nu\geq 4\), where \(\nu\) is the index of \(\langle,\rangle\). If \(M\) is null holomorphically flat at \(p\in M\), then the author studies also sufficient conditions to have \(M\) of constant holomorphic curvature at \(p\). If \(M\) is null holomorphically flat at \(p\in M\) these conditions are expressed in terms of bounded from below (or above) curvatures of nondegenerate holomorphic planes in \((\text{span}\{z,Jz\})^ \perp\). The author studies these sufficient conditions in terms of bounded curvatures of anti-holomorphic planes with signature \((-,+)\) or \((+,+)\) or \((-,-)\). Reviewer: N.Bokan (Beograd) MSC: 53C55 Global differential geometry of Hermitian and Kählerian manifolds Keywords:constant holomorphic sectional curvature; holomorphically flat PDFBibTeX XMLCite \textit{D. N. Kupeli}, Manuscr. Math. 80, No. 1, 1--12 (1993; Zbl 0804.53090) Full Text: DOI EuDML References: [1] Barros, M.; Romero, A., Indefinite Kähler Manifolds, Math. Ann., 261, 55-62 (1982) · Zbl 0476.53013 [2] Küpeli, D.N.: “On Curvatures of Indefinite Kähler metrics”. Preprint Series, METU Math. Dept. No:92/48 · Zbl 0844.53016 [3] O’Neill, B., Semi-Riemannian Geometry (1983), New York: Academic Press, New York · Zbl 0531.53051 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.