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Four-dimensional Kähler metrics admitting c-projective vector fields

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journal contribution
posted on 16.06.2015, 13:01 by Alexey Bolsinov, Vladimir S. Matveev, Thomas Mettler, Steffan Rosemann
A vector field on a Kähler manifold is called c-projective if its flow preserves the J-planar curves. We give a complete local classification of Kähler real 4-dimensional manifolds that admit an essential c-projective vector field. An important technical step is a local description of 4-dimensional c-projectively equivalent metrics of arbitrary signature. As an application of our results we prove the natural analog of the classical Yano-Obata conjecture in the pseudo-Riemannian 4-dimensional case.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal des Mathematiques Pures et Appliquees

Volume

103

Issue

3

Pages

619 - 657

Citation

BOLSINOV, A.V. et al, 2015. Four-dimensional Kähler metrics admitting c-projective vector fields. Journal des Mathematiques Pures et Appliquees, 103 (3), pp.619-657

Publisher

© Elsevier Masson SAS

Version

AM (Accepted Manuscript)

Publisher 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/

Publication date

2015

ISSN

0021-7824

eISSN

1776-3371

Language

en

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