Umbilic foliations with integrable normal bundle

In this paper we study the geometric properties of a couple of mutually orthogonal foliations with complementary dimensions. We recall that from Novikov's theorem, there is no foliation of S3 by closed curves with integrable normal bundle. Nevertheless, for S2k+1, k≥2, Novikov's theorem is not applicable. In this paper we show that on odd-dimensional unit spheres there is no umbilical foliation with integrable normal bundle and divergence free mean curvature vector.