  We consider a general n dimensional manifold, which is a direct product
manifold of $M^4 \times M^{n-4}$ representing our universe and extra spatial
dimensions. From Einstein-Hilbert action of the manifold, we deduce effective 4
dimensional Fridemann equations. Matching it with the normal Fridemann
equations with the cosmological constant, we give an expression of the
cosmological constant, and the expression under different conditions are
discussed. Also according to a deduced relation, we reveal a connection between
Hubble parameter and extra dimensions. In this regard, we take into account all
possible states of extra dimension which are consistent with current
experimental result as well.
