  The spatial structure of the spinor Bose-Einstein condensates with the spin
degrees of freedom is analyzed based on the generalized Gross-Pitaevskii
equation (GP) in the light of the present spin domain experiment on m_F=\pm 1,
and 0 of the hyperfine state F=1 of ^{23}Na atom gases. The GP solutions in
three- and one-spatial dimensional cases reproduce the observed spin domain
structures, revealing the length scale associated with the existence of the
weak interaction of the spin-spin channel, other than the ordinary coherence
length related to the density-density channel. The obtained domain structure in
GP is compared with the result in Thomas-Fermi approximation. The former
solution is found to better describe the observed features than the latter.
