BOLSINOV, A.V. and ROSEMANN, S., 2018. Local description of Bochner-flat (pseudo-)Kahler metrics. Communications in Analysis and Geometry, In Press.
The Bochner tensor is the Kahler 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-)Kahler 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 Kahler-Einstein metrics admitting a c-projectively equivalent one.
This paper is in closed access.
The work of the first author was supported by the Russian Science Foundation (grant No. 17-11-01303). The second author thanks Deutsche Forschungsgemeinschaft (Research training group 1523 — Quantum and Gravitational Fields), Friedrich-Schiller-Universit¨at Jena and Leibniz Universit¨at Hannover for partial financial support.