We consider a class of new field equations and present general solution of these equations. These equations are invariant under orthogonal coordinate transformations and invariant under gauge transformations, which depend on some Lie groups. We use some new geometrical objects - Clifford field vector and an algebra of h-forms which is a generalization of the Atiyah-Kahler algebra and the algebra of differential forms. With the use of new field equations we present a class of covariantly constant solutions of the Yang-Mills equations.
The reported study was funded by Russian Science Foundation (project RSF 14-11-00687, Steklov Mathematical Institute) and by RFBR according to the research project No. 16-31-00347 mol_a.