  We show that attractive spinor Bose-Einstein condensates under the action of
spin-orbit coupling (SOC) and Zeeman splitting form self-sustained stable two-
and three-dimensional (2D and 3D) states in free space, even when SOC acts in a
lower-dimensional form. We find that two-dimensional states are stabilized by
one-dimensional (1D) SOC in a broad range of chemical potentials, for atom
numbers (or norm of the spinor wavefunction) exceeding a threshold value, which
strongly depends on the SOC strength and vanishes at a critical point. The
zero-threshold point is a boundary between single-peaked and striped states,
realizing hybrids combining 2D and 1D structural features. In a vicinity of
such point, an asymptotic equation describing the bifurcation of the solitons
from the linear spectrum is derived and investigated analytically. We show that
striped 3D solitary states are as well stabilized by 2D SOC, albeit in a
limited range of chemical potentials and norms.
