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arXiv · 1709.08877

Local description of Bochner-flat (pseudo-)Kähler metrics

Alexey V. Bolsinov·Stefan Rosemann
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Abstract

The Bochner tensor is the Kähler analogue of the conformal Weyl tensor. In this article, we derive local (i.e., in a neighbourhood of almost every point) normal forms for a (pseudo-)Kähler manifold with vanishing Bochner tensor. The description is pined down to a new class of symmetric spaces which we describe in terms of their curvature operators. We also give a local description of weakly Bochner-flat metrics defined by the property that the Bochner tensor has vanishing divergence. Our results are based on the local normal forms for c-projectively equivalent metrics. As a by-product, we also describe all Kähler-Einstein metrics admitting a c-projectively equivalent one.

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BibTeXRIS

Alexey V. Bolsinov, Stefan Rosemann. 2017-09-26. Local description of Bochner-flat (pseudo-)Kähler metrics. https://arxiv.org/abs/1709.08877

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