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arXiv · 1710.00235

Conformally Kähler, Einstein--Maxwell metrics and boundedness of the modified Mabuchi-functional

Abdellah Lahdili
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Abstract

We prove that if a compact smooth polarized complex manifold admits in the corresponding Hodge Kähler class a conformally Kähler, Einstein--Maxwell metric, or more generally, a Kähler metric of constant $(ξ, a, p)$-scalar curvature, then this metric minimizes the $(ξ,a,p)$-Mabuchi functional. Our method of proof extends the approach introduced by Donaldson and developed by Li and Sano--Tipler, via finite dimensional approximations and generalized balanced metrics. As an application of our result and the recent construction of Koca--Tønnesen-Friedman, we describe the Kähler classes on a geometrically ruled complex surface of genus greater than 2, which admit conformally Kähler, Einstein-Maxwell metrics.

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Abdellah Lahdili. 2018-09-21. Conformally Kähler, Einstein--Maxwell metrics and boundedness of the modified Mabuchi-functional. https://arxiv.org/abs/1710.00235

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