1206.3941 (Mustafa Kalafat et al.)

Einstein-Hermitian 4-Manifolds of Positive Bisectional Curvature    [PDF]

Mustafa Kalafat, Caner Koca

We show that a compact complex surface together with an Einstein-Hermitian metric of positive holomorphic bisectional curvature is biholomorphically isometric to the complex projective plane with its Fubini-Study metric up to rescaling. This result relaxes the Kaehler condition in Berger's theorem (1965), and the positivity condition on sectional curvature in a theorem proved by Koca.

View original: http://arxiv.org/abs/1206.3941