  We consider Bianchi VI spacetime, which also can be reduced to Bianchi types
VI0-V-III-I. We initially consider the most general form of the energy-momentum
tensor which yields anisotropic stress and heat flow. We then derive an
energy-momentum tensor that couples with the spatial curvature in a way so as
to cancel out the terms that arise due to the spatial curvature in the
evolution equations of the Einstein field equations. We obtain exact solutions
for the universes indefinetly expanding with constant mean deceleration
parameter. The solutions are beriefly discussed for each Bianchi type. The
dynamics of the models and fluid are examined briefly, and the models that can
approach to isotropy are determined. We conclude that even if the observed
universe is almost isotropic, this does not necessarily imply the isotropy of
the fluid (e.g., dark energy) affecting the evolution of the universe within
the context of general relativity.
