Abstract
In this paper we prove that special requirements to Yang-Mills equations on a 4-dimensional conformally connected manifold allow one to reduce them to a system of Einstein equations and additional ones that bind components of the energy-impulse tensor. We propose an algorithm that gives conditions for the embedding of the metric of the gravitational field into a special (uncharged) Yang-Mills conformally connected manifold. As an application of the algorithm, we prove that the metric of any Einstein space and the Robertson-Walker metric are embeddable into the specified manifold.
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Original Russian Text © L.N. Krivonosov and V.A. Luk’yanov, 2009, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, No. 9, pp. 69–74.
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Krivonosov, L.N., Luk’yanov, V.A. The relationship between the Einstein and Yang-Mills equations. Russ Math. 53, 62–66 (2009). https://doi.org/10.3103/S1066369X09090072
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DOI: https://doi.org/10.3103/S1066369X09090072