Four-dimensional K\"ahler metrics admitting c-projective vector fields
Differential Geometry
2015-10-07 v1
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.
Cite
@article{arxiv.1311.0517,
title = {Four-dimensional K\"ahler metrics admitting c-projective vector fields},
author = {Alexey V. Bolsinov and Vladimir S. Matveev and Thomas Mettler and Stefan Rosemann},
journal= {arXiv preprint arXiv:1311.0517},
year = {2015}
}
Comments
33 pages, 2 figures