Compact orbits of smooth Killing vector fields on Riemannian manifolds (Q5928676)

The author studies orbits of a family \(\mathcal F\) of smooth Killing vector fields on a Riemannian manifold. It is shown that the family of zero-time orbits of a compact orbit \(N\) of \(\mathcal F\) forms a Riemannian foliation of \(N\). Furthermore, only two possibilities can occur: either all zero-time orbits are dense in \(N\) or they are fibers of a locally trivial fibration \(N\to S^1\).