Mean curvature functions of codimension-one foliations. II (Q1190205)

Let \(F\) be a given transversely oriented codimension-one foliation on a closed oriented manifold \(M\). The author gives a new necessary and sufficient condition for a smooth function on \(M\) to be the mean curvature function of \(F\) with respect to some Riemannian metric on \(M\). This affirmatively settles a conjecture by the author in part I [ibid. 65, No. 1, 79-84 (1990; Zbl 0704.53023)]. In consequence, he gives a topological characterization of codimension-one foliations consisting of constant mean curvature hypersurfaces.