  We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory on
spaces of the form R x SU(3)/H, with H equals either SU(2) x U(1) or U(1) x
U(1). For the corresponding quiver gauge theory we derive the equations of
motion and construct some specific solutions for the Higgs fields using
different gauge groups. Specifically we choose the gauge groups U(6) and U(8)
for the space R x CP^2 as well as the gauge group U(3) for the space R x
SU(3)/U(1)xU(1), and derive Yang-Mills equations for the latter one using a
spin connection endowed with a non-vanishing torsion. We find that a specific
value for the torsion is necessary in order to obtain non-trivial solutions of
Yang-Mills equations. Finally, we take the space R x CP^1 x CP^2 and derive the
equations of motion for the Higgs sector for a U(3m+3) gauge theory.
