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.
Keywords
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