Cohomogeneity one disk bundles with normal homogeneous collars
Differential Geometry
2014-02-26 v1
Abstract
We consider cohomogeneity one homogeneous disk bundles and adress the question when these admit a nonnegatively curved invariant metric with normal collar, i.e., such that near the boundary the metric is the product of an interval and a normal homogeneous space. If such a bundle is not (the quotient of) a trivial bundle, then we show that its rank has to be in . Moreover, we give a complete classification of such bundles of rank 6 and 8, and a partial classification for rank 3.
Cite
@article{arxiv.0806.3824,
title = {Cohomogeneity one disk bundles with normal homogeneous collars},
author = {Lorenz J. Schwachhoefer and Kristopher Tapp},
journal= {arXiv preprint arXiv:0806.3824},
year = {2014}
}