On Conformally Kaehler, Einstein Manifolds
Differential Geometry
2007-06-13 v2 General Relativity and Quantum Cosmology
Algebraic Geometry
Analysis of PDEs
Abstract
We prove that any compact complex surface with positive first Chern class admits an Einstein metric which is conformally related to a Kaehler metric. The key new ingredient is the existence of such a metric on the blow-up of the complex projective plane at two distinct points.
Cite
@article{arxiv.0705.0710,
title = {On Conformally Kaehler, Einstein Manifolds},
author = {Xiuxiong Chen and Claude LeBrun and Brian Weber},
journal= {arXiv preprint arXiv:0705.0710},
year = {2007}
}