In this paper, we study the asymptotic symmetry and local behavior of positive solutions at infinity to the equation outside a bounded set in Rn, where Rn/3, Laplacian with asymptotically flat Riemannian metric g. We prove that the solution, at1, either converges to a fundamental solution of the Laplace operator on the Euclidean space, or is asymptotically close to a Fowler-type solution defined on Rn/3.