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Local description of Bochner-flat (pseudo-)Kähler metrics
journal contribution
posted on 2021-06-09, 15:23 authored by Alexey BolsinovAlexey Bolsinov, Stefan RosemannThe 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.
Funding
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.
History
School
- Science
Department
- Mathematical Sciences
Published in
Communications in Analysis and GeometryVolume
29Issue
3Pages
525-577Citation
BOLSINOV, A.V. and ROSEMANN, S., 2021. Local description of Bochner-flat (pseudo-)Kähler metrics. Communications in Analysis and Geometry, 29 (3), pp.525-577.Publisher
International PressVersion
- AM (Accepted Manuscript)
Rights holder
© International PressPublisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Acceptance date
2018-09-24Publication date
2021-05-10Copyright date
2021ISSN
1019-8385Publisher version
Language
- en