  We construct a set of exact ground states with a localized ferromagnetic
domain wall and with an extended spiral structure in a deformed flat-band
Hubbard model in arbitrary dimensions. We show the uniqueness of the ground
state for the half-filled lowest band in a fixed magnetization subspace. The
ground states with these structures are degenerate with all-spin-up or
all-spin-down states under the open boundary condition. We represent a spin
one-point function in terms of local electron number density, and find the
domain wall structure in our model. We show the existence of gapless
excitations above a domain wall ground state in dimensions higher than one. On
the other hand, under the periodic boundary condition, the ground state is the
all-spin-up or all-spin-down state. We show that the spin-wave excitation above
the all-spin-up or -down state has an energy gap because of the anisotropy.
