2005/08/21 by Kristopher Tapp, Tapp, Kristopher
Mathematics · Physics and Astronomy · #53C20 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG) #math.DG #math.MG #msc:53C20
paper · pdf · doi:10.48550/arxiv.math/0508394
arxiv created 2005/08/21 · openalex publication_date 2005/08/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Examples of almost-positively and quasi-positively curved spaces of the form M=H((G,h)xF) were discovered recently. Here, h is a left-invariant metric on a compact Lie group G, F is a compact Riemannian manifold on which the subgroup H of G acts isometrically on the left, and M is the orbit space of the diagonal left action of H on (G,h)xF with the induced Riemannian submersion metric. We prove that no new examples of strictly positive sectional curvature exist in this class of metrics. This result generalizes the case F=point proven by Geroch.