Caner Koca

Strongly Hermitian Einstein–Maxwell solutions on ruled surfaces

This paper produces explicit strongly Hermitian Einstein–Maxwell solutions on the smooth compact 4-manifolds that are

Conformally Kähler surfaces and orthogonal holomorphic bisectional curvature

S^2

On the curvature of Einstein-Hermitian Surfaces

S2-bundles over compact Riemann surfaces of any genus. This generalizes the existence results by LeBrun (J Geom Phys 91:163–171, 2015, The Einstein–Maxwell equations and conformally Kaehler geometry. arXiv:1504.06669, 2016). Moreover, by calculating the (normalized) Einstein–Hilbert functional of our examples, we generalize Theorem E of LeBrun (The Einstein–Maxwell equations and conformally Kaehler geometry. arXiv:1504.06669, 2016), which speaks to the abundance of Hermitian Einstein–Maxwell solutions on such manifolds. As a bonus, we exhibit certain pairs of strongly Hermitian Einstein–Maxwell solutions, first found in LeBrun (The Einstein–Maxwell equations and conformally Kaehler geometry. arXiv:1504.06669, 2016), on the first Hirzebruch surface in a form which clearly shows that they are conformal to a common Kähler metric. In particular, this yields a non-trivial example of non-uniqueness of positive constant scalar curvature metrics in a given conformal class.

Einstein-Hermitian 4-Manifolds of Positive Bisectional Curvature

In this paper we will prove that the only compact 4-manifold M with an Einstein metric of positive sectional curvature which is also hermitian with respect to some complex structure on M, is the complex projective plane CP^2, with its Fubini-Study metric.

On Conformal Geometry of Kahler Surfaces

We show that a compact complex surface which admits a conformally Kähler metric

Complex Surfaces of Locally Conformally Flat Type

g