2021
DOI: 10.48550/arxiv.2111.00294
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Globally conformally Kähler Einstein metrics on certain holomorphic bundles

Abstract: The subject of this paper is the explicit momentum construction of complete Einstein metrics by ODE methods. Using the Calabi ansatz, further generalized by Hwang-Singer, we show that there are non-trivial complete conformally Kähler Einstein metrics on certain Hermitian holomorphic vector bundles and their subbundles over complete Kähler-Einstein manifolds. In special cases, we give the explicit expressions of of these metrics. These examples show that there is a compact Kähler manifold M and its subvariety N… Show more

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