Compact Hermitian surfaces of constant antiholomorphic sectional curvatures

Apostolov, Vestislav; Ganchev, Georgi; Ivanov, Stefan

doi:10.1090/S0002-9939-97-04043-4

Compact Hermitian surfaces of constant antiholomorphic sectional curvatures
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by Vestislav Apostolov, Georgi Ganchev and Stefan Ivanov

Proc. Amer. Math. Soc. 125 (1997), 3705-3714

DOI: https://doi.org/10.1090/S0002-9939-97-04043-4

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Abstract:

Compact Hermitian surfaces of constant antiholomorphic sectional curvatures 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 Kaehler surface; a compact Hermitian surface of constant antiholomorphic Hermitian sectional curvatures is either a Kaehler surface of constant (non-zero) holomorphic sectional curvatures or a conformally flat Hermitian surface.

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