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Complex Surfaces and Null Conformal Killing Vector Fields

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Abstract

We study the relation between the existence of null conformal Killing vector fields and the 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 the 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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Acknowledgements

The first and the third named authors are partially supported by the Bulgarian National Science Fund, Ministry of Education and Science of Bulgaria under Contract KP-06-N52/3. The second named author is supported by the Simons Foundation Collaboration Grant Number 853269. He wants to express his gratitude to the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences, Sofia for the warm hospitality during his visits to work on the project.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    J. Davidov & O. Mushkarov

  2. Department of Mathematics, Florida International University, Miami, FL, 33199, USA

    G. Grantcharov

  3. Sauth-West University, 2700, Blagoevgrad, Bulgaria

    O. Mushkarov

Authors
  1. J. Davidov
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  2. G. Grantcharov
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  3. O. Mushkarov
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Correspondence to G. Grantcharov.

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Davidov, J., Grantcharov, G. & Mushkarov, O. Complex Surfaces and Null Conformal Killing Vector Fields. J Geom Anal 33, 224 (2023). https://doi.org/10.1007/s12220-023-01265-2

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