On the orbit structure of ℝ n onn-manifolds

Abstract

We begin by proving that a locally freeC 2-action of ℝ n-1 onT n−1×[0,1] tangent to the boundary and without compact orbits in the interior has all non-compact orbits of the same topological type. Then, we consider the setA 2(ℝ n ,N) ofC 2-actions of ℝ n on a closed connected orientable real analyticn-manifoldN. We define a subsetA n ⊂A r (ℝ n ,N) and prove that if φ∈A n has aT n-1 x ℝ-orbit, then everyn-dimensional orbit is also aT n-1 x ℝ-orbit. The subsetA n , is big enough to contain all real analytic, actions that have at least onen-dimensional orbit. We also obtain information on the topology ofN.