  We analytically and numerically investigate the ground state of the
spin-orbit coupled spin-1 Bose-Einstein condensates in an external parabolic
potential. When the spin-orbit coupling strength $\kappa$ is comparable with
that of the trapping potential, the density distribution centers of different
components of the spinor condensate deviate evidently from the trap center in
the plane wave and stripe phases. When $\kappa\gg1$, the magnitude of this
deviation decreases as $\kappa$ is getting larger and larger. Correspondingly,
periphery half-skyrmions textures arise. This deviation can be reflected by the
non-uniform magnetic moment in the $z$ direction, $\mathcal{F}_z$. With the
manipulation of the external trap, the local magnitude of $\mathcal{F}_z$ can
be increased evidently. This kind of increase of $\mathcal{F}_z$ is also
observed in the square vortex lattice phase of the condensate.
