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Compact Hermitian surfaces of constant antiholomorphic sectional curvatures. (English) Zbl 0898.53025

Authors’ abstract: “Compact Hermitian surfaces of constant antiholomorphic sectional curvature with respect to the Riemannian curvature tensor and with respect to the Hermitian curvature tensor are considered. It is proved: a compact Hermitian surface of constant antiholomorphic Riemannian sectional curvatures is a self-dual Kähler surface; a compact Hermitian surface of constant antiholomorphic Hermitian sectional curvatures is either a Kähler surface of constant (non-zero) holomorphic sectional curvatures or a conformally flat Hermitian surface”.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
53B35 Local differential geometry of Hermitian and Kählerian structures
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