2008/06/24 by Lorenz Schwachhöfer, Lorenz J. Schwachhoefer, Kristopher Tapp · 6 citations
Mathematics · #Boundary (topology) #Bundle #Combinatorics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homogeneous #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Mathematical analysis #Mathematics #Pure mathematics #Quotient #Rank (graph theory) #Vector bundle #math.DG #msc:53Cxx
paper · pdf · doi:10.1112/plms/pdp012
published in Proceedings of the London Mathematical Society 99(3), 609-632 (Wiley)
arxiv created 2008/06/24 · openalex publication_date 2009/04/24 · arxiv updated 2014/02/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider cohomogeneity one homogeneous disk bundles and address the question when these admit a nonnegatively curved† invariant metric with normal collar, that is, 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.