Conformally Kähler surfaces and orthogonal holomorphic bisectional curvature
arXiv:1410.5001 · doi:10.1007/s10711-014-0025-9
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.
12 pages. Journal information added