Nontaut foliations and isoperimetric constants
Tom 78 / 2002
Annales Polonici Mathematici 78 (2002), 97-110 MSC: Primary 53C12. DOI: 10.4064/ap78-2-1
We study nontaut codimension one foliations on closed Riemannian manifolds. We find an estimate of some constant derived from the mean curvature function of the leaves of a foliation by some isoperimetric constant of the manifold. Moreover, for foliated 2-tori and the 3-dimensional unit sphere, we find the infimum of the former constants for all nontaut codimension one foliations.