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arXiv · 1410.5001

Conformally Kähler surfaces and orthogonal holomorphic bisectional curvature

Mustafa Kalafat·Caner Koca
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Abstract

We show that a compact complex surface which admits a conformally Kähler metric g of positive orthogonal holomorphic bisectional curvature is biholomorphic to the complex projective plane. In addition, if g is a Hermitian metric which is Einstein, then the biholomorphism can be chosen to be an isometry via which g becomes a multiple of the Fubini-Study metric.

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Mustafa Kalafat, Caner Koca. 2015-04-06. Conformally Kähler surfaces and orthogonal holomorphic bisectional curvature. https://doi.org/10.1007/s10711-014-0025-9

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