English

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 {2,3,4,6,8}\{2,3,4,6,8\}. Moreover, we give a complete classification of such bundles of rank 6 and 8, and a partial classification for rank 3.

Keywords

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}
}
R2 v1 2026-06-21T10:53:42.968Z