Find Paper, Faster
Example:10.1021/acsami.1c06204 or Chem. Rev., 2007, 107, 2411-2502
Local description of Bochner-flat (pseudo-)Kähler metrics
Communications in Analysis and Geometry  (IF0.736),  Pub Date : 2021-05-01, DOI: 10.4310/cag.2021.v29.n3.a1
Alexey V. Bolsinov, Stefan Rosemann

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 byproduct, we also describe all Kähler–Einstein metrics admitting a $c$-projectively equivalent one.