On killing fields preserving minimal foliations of polynomial growth at most 2

Abstract

Let $\mathscr{F}$ be a minimal foliation of a complete Riemannian manifold (M, g). Assume that the orthogonal distribution to $\mathscr{F}$ is also integrable. We show that if the growth of $\mathscr{F}$ is at most 2 then any Killing field with bounded length preserves the foliation $mathscr{F}$.