  We show several kinematical properties that are intrinsic to the Bianchi
models with compact spatial sections. Especially, with spacelike hypersurfaces
being closed, (A) no anisotropic expansion is allowed for Bianchi type V and
VII(A\not=0), and (B) type IV and VI(A\not=0,1) does not exist. In order to
show them, we put into geometric terms what is meant by spatial homogeneity and
employ a mathematical result on 3-manifolds. We make clear the relation between
the Bianchi type symmetry of space-time and spatial compactness, some part of
which seem to be unnoticed in the literature. Especially, it is shown under
what conditions class B Bianchi models do not possess compact spatial sections.
Finally we briefly describe how this study is useful in investigating global
dynamics in (3+1)-dimensional gravity.
