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Rosa Sena Dias - Conformally Kähler, Einstein Metrics from ODEs

Abstract: Einstein metrics have played a fundamental role in geometry. One of the main sources of examples of Einstein metrics has been Kähler geometry. Yet we know that several Kähler manifolds do not carry Kähler-Einstein metrics. In the 80’s, Derdziński obtained a local construction for 4d conformally Kähler, Einstein metrics using extremal Kähler metrics. Together with G. Oliveira, we set out to use Derdziński’s methods on a class of extremal Kähler metrics arising from an ansatz due to Calabi. In this talk, I shall report on our findings. I will start by giving background on Einstein metrics, Kähler geometry, and Derdziński’s construction. Calabi’s metrics arise from an ODE, and I will explain how this plays a role.