English

Conformally K\"ahler surfaces and orthogonal holomorphic bisectional curvature

Differential Geometry 2015-04-07 v2 Mathematical Physics math.MP

Abstract

We show that a compact complex surface which admits a conformally K\"ahler 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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Cite

@article{arxiv.1410.5001,
  title  = {Conformally K\"ahler surfaces and orthogonal holomorphic bisectional curvature},
  author = {Mustafa Kalafat and Caner Koca},
  journal= {arXiv preprint arXiv:1410.5001},
  year   = {2015}
}

Comments

12 pages. Journal information added