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Title: Four-dimensional Kähler metrics admitting c-projective vector fields
Authors: Bolsinov, Alexey V.
Matveev, Vladimir S.
Mettler, Thomas
Rosemann, Steffan
Keywords: C-Projective geometry
Hamiltonian 2-forms
Kähler geometry
Issue Date: 2015
Publisher: © Elsevier Masson SAS
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
Abstract: 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.
Version: Accepted for publication
DOI: 10.1016/j.matpur.2014.07.005
URI: https://dspace.lboro.ac.uk/2134/17886
Publisher Link: http://dx.doi.org/10.1016/j.matpur.2014.07.005
ISSN: 0021-7824
Appears in Collections:Published Articles (Maths)

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