Collapse of warped foliations (Q2472643)

The concept of warped product is generalized to foliated manifolds and the question of existence of the limit in Gromov-Hausdorff topology of a sequence of warped foliations is solved. Necessary and sufficient condition for convergence in Gromov-Hausdorff sense of a Riemannian foliation with all leaves compact to the space of leaves with a metric defined by Hausdorff distance of leaves is developed. Finally, some results on Hausdorff foliations with all leaves compact are shown.