The notion of the Hausdorffized leaf space of a foliation is introduced. A sufficient condition for warped compact foliations to converge to is given. Moreover, a necessary condition for warped compact Hausdorff foliations to converge to is shown. Finally, some examples are examined.
A Weitzenböck formula for SL(q)-foliations is derived. Its linear part is a relative trace of the relative curvature operator acting on vector valued forms.
We define Weyl submersions, for which we derive equations analogous to the Gauss and Codazzi equations for an isometric immersion. We obtain a necessary and sufficient condition for the total space of a Weyl submersion to admit an Einstein-Weyl structure. Moreover, we investigate the Einstein-Weyl structure of canonical variations of the total space with Einstein-Weyl structure.