In [2], H. Furstenberg studied a distal action of a locally compact group G on a compact metric space X, and established a structure theorem. As a consequence, he showed that if G is abelian, then a simply connected space X does not admit a minimal distal G-action.

In this paper we concern ourselves with a nonsingular flow ϕ={ϕt} on a closed 3-manifold M. Recall that ϕ is called distal if for any distinct two points x, y ∈ M, the distance d(ϕtx, ϕty) is bounded away from 0. The distality depends strongly upon the time parametrization. For example, there exists a time parametrization of a linear irrational flow on T2 which yields a nondistal flow [4, 6].