Totally geodesic foliations and Killing fields. II (Q1070544)

The author extends his results in part I [ibid. 35, 387-392 (1983; Zbl 0517.53035)] to higher codimensions as follows: Theorem. Let (M,g) be a connected complete Riemannian manifold and F be a totally geodesic foliation of (M,g). Assume that the bundle orthogonally complement to F is also integrable. Then any Killing field Z on (M,g) with bounded length, i.e., \(g(Z,Z)\leq const.<\infty\) on M, preserves F. Further, he studies a related topic concerning minimal foliations.