  We investigate a class of cosmological solutions of Einstein's field
equations in higher dimensions with a cosmological constant and an ideal fluid
matter distribution as a source. We discuss the dynamical evolution of the
universe subject to two constraints that (i) the total volume scale factor of
the universe is constant and (ii) the effective energy density is constant. We
obtain various interesting new dynamics for the external space that yield a
time varying deceleration parameter including oscillating cases when the
flat/curved external and curved/flat internal spaces are considered. We also
comment on how the universe would be conceived by an observer in four
dimensions who is unaware of the extra dimensions.
