Four-dimensional Kähler metrics admitting c-projective vector fields

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.

33 pages, 2 figures

Cited by in corpus (2)

• Conification construction for Kaehler manifolds and its application in c-projective geometry
• The c-projective symmetry algebras of Kähler surfaces