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

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

2007-06-14

arxiv.org/abs/0706.2051v1

Mathematics

Differential Geometry

9 pages

Scientific paper

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.

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