Cohomogeneity one disk bundles with normal homogeneous collars

Details Cohomogeneity one disk bundles with normal homogeneous collars Cohomogeneity one disk bundles with normal homogeneous collars

2008-06-24

arxiv.org/abs/0806.3824v1

Mathematics

Differential Geometry

Scientific paper

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

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