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

2007/06/14 by Wojciech Kozłowski, Wojciech Kozlowski, Kozlowski, Wojciech +2
Mathematics · Physics and Astronomy · #Mathematics and Applications #Planetary Science and Exploration #Point processes and geometric inequalities #math.DG #math.MG #msc:53B21 #msc:70G45

paper · pdf · doi:10.48550/arxiv.0706.2051

9 pages

arxiv created 2007/06/14 · arxiv updated 2009/12/01

Abstract

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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