Four-dimensional Kahler metrics admitting c-projective vector fields

A vector field on a Kahler manifold is called c-projective if its flow preserves the J-planar curves. We give a complete local classification of Kahler 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. (C) 2014 Elsevier Masson SAS. All rights reserved.