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

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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.
9 pages

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Differential Geometry, Metric Geometry, 53B21; 70G45

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http://salesiana.dossiersoluciones.com/handle/123456789/131722

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0706.2051
 http://arxiv.org/abs/0706.2051

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arXiv