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On Conformally Kaehler, Einstein Manifolds

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arxiv 0705.0710 v2 pith:3FDDHZMK submitted 2007-05-07 math.DG gr-qcmath.AGmath.AP

Xiuxiong Chen , Claude LeBrun , Brian Weber This is my paper · ORCID
classification math.DGgr-qcmath.AGmath.AP
keywords metriccomplexconformallyeinsteinkaehleradmitsblow-upchern
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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.

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  1. On Chen-Teo geometries with cosmological constant

    math.DG 2026-06 unverdicted novelty 6.0 of 10

    Einstein metrics extending Chen-Teo geometries with cosmological constant are either Plebański-Demiański or anti-self-dual Weyl cases, yielding for lambda<0 a conformal infinity between asymptotically hyperbolic ends,...

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