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arXiv · 2204.13770

Complex surfaces and null conformal Killing vector fields

Johann Davidov·Gueo Grantcharov·Oleg Mushkarov
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Abstract

We study the relation between the existence of null conformal Killing vector fields and existence of compatible complex and para-hypercomplex structures on a pseudo-Riemannian manifold with metric of signature (2,2). We establish first the topological types of pseudo-Hermitian surfaces admitting a nowhere vanishing null vector field. Then we show that a pair of orthogonal, pointwise linearly independent, null, conformal Killing vector fields defines a para-hyperhermitian structure and use this fact for a classification of the smooth compact four-manifolds admitting such a pair of vector fields. We also provide examples of neutral metrics with two orthogonal, pointwise linearly independent, null Killing vector fields on most of these manifolds.

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Johann Davidov, Gueo Grantcharov, Oleg Mushkarov. 2022-10-16. Complex surfaces and null conformal Killing vector fields. https://arxiv.org/abs/2204.13770

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