On v-Distal Flows on 3-Manifolds

In 2], H. Furstenberg studied a distal action of a locallycompact group G on a compact metric space X, and establisheda structure theorem. As a consequence, he showed that if G isabelian, then a simply connected space X does not admit a minimaldistal G-action. In this paper we concern ourselves with a nonsingular flow = {^t} on a closed 3-manifold M. Recall that is called distalif for any distinct two points x, y M, the distance d(^tx, ^ty)is bounded away from 0. The distality depends strongly uponthe time parametrization. For example, there exists a time parametrizationof a linear irrational flow on T² which yields a nondistal flow4, 6]. 1991 Mathematics Subject Classification 58F25, 57R30.