Purely time-dependent solutions to the Yang–Mills equations on a $4$-dimensional manifold with conformal torsion-free connection

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.