Geodesic
Purely time-dependent solutions to the Yang--Mills equations on a~$4$-dimensional manifold with conformal torsion-free connection
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 1, pp. 40-52

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We deduce the purely time-depending Yang–Mills equations in a space with conformal torsion-free connection. Next we find three series of solutions to these equations and study which of them give the Einstein metric or a metric conformally equivalent to it. Also, various representations of these solutions with and without singularities are presented.
Keywords: Einstein equations, Maxwell's equations, Yang–Mills equations, manifold with conformal connection. 
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Leonid N. Krivonosov; Vyacheslav A. Lukyanov. Purely time-dependent solutions to the Yang--Mills equations on a~$4$-dimensional manifold with conformal torsion-free connection. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 1, pp. 40-52. http://geodesic.mathdoc.fr/item/JSFU_2013_6_1_a4/