  The covariantly constant gauge fields are solutions of the sourceless
Yang-Mills equation and represent the classical vacuum fields. We found that
the moduli space of covariantly constant gauge fields is much larger than the
space of constant chromomagnetic fields. A wider class of covariantly constant
gauge field solutions representing non-perturbative magnetic flux sheets of
finite thickness is obtained through the nontrivial space-time dependence of a
unit colour vector. In some sense these solutions are similar to the
Nielsen-Olesen magnetic flux tubes, but instead they have geometry of magnetic
flux sheets and are supported without presence of any Higgs field. The
infinitesimally thin magnetic sheet solutions can be associated with the
singular surfaces considered by 't Hooft. The nonlocal operators that are
supported on a two-dimensional surface rather than a one-dimensional curve were
considered in literature. These surface operators are analogous to Wilson W(C)
and 't Hooft line operators M(C) except that they are supported on a
two-dimensional surface rather than a one-dimensional curve. The class of
non-perturbative solutions representing a nonvanishing chromomagnetic field
that fills out the whole 3D-space is obtained as well. This new class of
covariantly constant gauge field solutions is constructed by using the general
properties of the Cho Ansatz. We define the topological currents and the
corresponding charges and demonstrate that the new solutions have a zero
monopole charge density. Instead, the solutions have a nonzero Hopf invariant,
which is the magnetic helicity of the Faraday force lines.
