  We have constructed gravity solutions by breaking the Lorentzian symmetry to
its subgroup, which means there is Galilean symmetry but without the rotational
and boost invariance. This solution shows anisotropic behavior along both the
temporal and spatial directions as well as among the spatial directions and
more interestingly, it displays the precise scaling symmetry required for
metric as well as the form fields. From the field theory point of view, it
describes a theory which respects th5Ae scaling symmetry, $t\to \lambda^{z_1}t,
x\to \lambda^{z_2}t, y\to \lambda y$, for $z_1\neq z_2$, as well as the
translational symmetry associated to both time and space directions, which
means we have found a non-rotational but Lifshitz-like fixed points from the
dual field theory point of view. We also discuss the minimum number of
generators required to see the appearance of such Lifshitz points. In 1+1
dimensional field theory, it is 3 and for 2+1 dimensional field theory, the
number is 4.
