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We study unit horizontal bundles associated with Riemannian submersions.First we investigate metric properties of an arbitrary unit horizontal bundleequipped with a Riemannian metric of the Cheeger-Gromoll type. Next we examineit from the Gromov-Hausdorff convergence theory point of view, and we state acollapse theorem for unit horizontal bundles associated with a sequence ofwarped Riemannian submersions.

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