Bochner-flat（伪）Kähler度量的局部描述
Local description of Bochner-flat (pseudo-)Kähler metrics
摘要：
Bochner张量是共形Weyl张量的Kähler模拟。在这篇文章中，我们推导出本地（即，在几乎每一点的邻域内）正规形。的描述被钉到一类新的对称空间，我们描述他们的曲率算子。我们还给出了弱Bochner平坦度量的局部描述定义的性质，Bochner张量有消失的发散。我们的结果是基于局部正规形的c-射影等价度量。作为一个副产品，我们还描述了所有的凯勒-爱因斯坦度量承认一个c-投射等价的。
英文摘要：
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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