  We discuss role of partially gravitating scalar fields, scalar fields whose
energy-momentum tensors vanish for a subset of dimensions, in dynamical
compactification of a given set of dimensions. We show that the resulting
spacetime exhibits a factorizable geometry consisting of usual four-dimensional
spacetime with full Poincare invariance times a manifold of extra dimensions
whose size and shape are determined by the scalar field dynamics. Depending on
the strength of its coupling to the curvature scalar, the vacuum expectation
value (VEV) of the scalar field may or may not vanish. When its VEV is zero the
higher dimensional spacetime is completely flat and there is no
compactification effect at all. On the other hand, when its VEV is nonzero the
extra dimensions get spontaneously compactified. The compactification process
is such that a bulk cosmological constant is utilized for curving the extra
dimensions.
