On Killing fields preserving minimal foliations of polynomial growth at most 2 (Q763974)

Let \((M,g)\) be a complete Riemannian manifold foliated by a minimal foliation \(\mathcal F\) whose orthogonal distribution is integrable. The author proves that if every leaf of \(\mathcal F\) has polynomial growth of at most second order, then any Killing vector field with bounded length preserves \(\mathcal F\), i. e. maps leaves to leaves. As a corollary it is proved that if \(\mathcal F\) is a minimal foliation of the Euclidean space \((E^{n},g_0)\) such that its orthogonal distribution \(\mathcal H\) is integrable and the growth of \(\mathcal F\) is at most \(2\), then \(\mathcal F\) and \(\mathcal H\) are totally geodesic foliations.