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Lorentzian Symmetric Spaces Which are Einstein–Yang–Mills with Respect to Invariant Metric Connections

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Abstract

We classify four-dimensional connected simply-connected Lorentzian symmetric spaces M with connected nontrivial isotropy group furnishing solutions of the Einstein–Yang–Mills equations. Those solutions are built with respect to some invariant metric connection \(\Lambda \) in the bundle of orthonormal frames of M and some diagonal metric on the holonomy algebra corresponding to \(\Lambda \).

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Acknowledgements

We are grateful to the referee by his/her valuable observations, which have contributed to improve this paper. We are indebted to Professor G. Calvaruso for the initial work we did on the topic and his recent rewarding suggestions, which have contributed to meliorate the manuscript. Our hearty thanks to Professor A. Elduque for his worthful help on several questions.

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Authors and Affiliations

  1. Departamento de Álgebra, Geometría y Topología, Facultad de Matemáticas, UCM, Plaza de Ciencias 3, 28040, Madrid, Spain

    Marco Castrillón López

  2. Instituto de Física Fundamental, CSIC, Serrano 113 bis, 28006, Madrid, Spain

    P. M. Gadea

  3. Departamento de Matemática Aplicada, Escuela Técnica Superior de Arquitectura, Universidad Politécnica de Madrid, Avda. Juan de Herrera 4, 28040, Madrid, Spain

    María Eugenia Rosado María

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  1. Marco Castrillón López
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  2. P. M. Gadea
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  3. María Eugenia Rosado María
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Correspondence to María Eugenia Rosado María.

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Research supported by the Ministerio de Ciencia, Innovación y Universidades, Spain: M.C.L. and E.R.M. under Project No. PGC2018-098321-B-I00; and P.M.G. under the MINECO-FEDER Grant MTM2016-77093-P.

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Castrillón López, M., Gadea, P.M. & Rosado María, M.E. Lorentzian Symmetric Spaces Which are Einstein–Yang–Mills with Respect to Invariant Metric Connections. Results Math 75, 143 (2020). https://doi.org/10.1007/s00025-020-01259-4

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