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arXiv · 1311.0517

Four-dimensional K\"ahler metrics admitting c-projective vector fields

Alexey V. Bolsinov·Vladimir S. Matveev·Thomas Mettler·Stefan Rosemann
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Abstract

A vector field on a K\"ahler manifold is called c-projective if its flow preserves the J-planar curves. We give a complete local classification of K\"ahler 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.

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Alexey V. Bolsinov, Vladimir S. Matveev, Thomas Mettler, Stefan Rosemann. 2013-11-03. Four-dimensional K\"ahler metrics admitting c-projective vector fields. https://doi.org/10.1016/j.matpur.2014.07.005

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