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arXiv · 1610.02078

On 2-dimensional Kaehler metrics with one holomorphic isometry

Samuele Chimento·Tomas Ortin
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Abstract

We show how to write any Kaehler metric of complex dimension 2 admitting a holomorphic isometry as a simple 1-real-function deformation of a Gibbons-Hawking metric. Hyper-Kaehler metrics with a tri-holomorphic isometry (Gibbons-Hawking metrics) or with a mono-holomorphic isometry are recovered for particular values of the additional function. The new general metric can be used as an Ansatz in several interesting physical problems.

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Samuele Chimento, Tomas Ortin. 2016-11-28. On 2-dimensional Kaehler metrics with one holomorphic isometry. https://arxiv.org/abs/1610.02078

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