Collapse of unit horizontal bundles equipped with a metric of Cheeger–Gromoll type

We study unit horizontal bundles associated with Riemannian submersions. First we investigate metric properties of an arbitrary unit horizontal bundle equipped with a Riemannian metric of the Cheeger–Gromoll type. Next we examine it from the Gromov–Hausdorff convergence theory point of view, and we state a collapse theorem for unit horizontal bundles associated with a sequence of warped Riemannian submersions.