  We present the interesting case of the 2+1 nonprojectable Horava theory
formulated at the critical point, where it does not posses local degrees of
freedom. The critical point is defined by the value of a coupling constant of
the theory. We discuss how, in spite of the absence of degrees of freedom, the
theory admits solutions with nonflat or nonconstant curvature. We consider the
theory without cosmological constant and without terms of higher order
derivatives, hence this is an effect that can be seen at the same order of 2+1
general relativity. We present an exact nonflat solution that is not
asymptotically flat. The presence of solutions with nontrivial curvature seems
to be related to the relaxing of the asymptotically flat condition. We discuss
that there is no analogue of Newtonian potential in this theory, and a broad
class of asymptotically flat geometries leads to the restriction that the only
solutions that can be found among them are the flat ones.
