2008/04/23 by Lorenz Schwachhöfer, Lorenz Schwachhofer, Schwachhofer, Lorenz +2 · 1 citation
Mathematics · Physics and Astronomy · #53Cxx #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:53Cxx
paper · pdf · doi:10.48550/arxiv.0804.3729
openalex publication_date 2008/04/23 · arxiv created 2008/06/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given compact Lie groups H⊂ G, we study the space of G-invariant metrics on G/H with nonnegative sectional curvature. For an intermediate subgroup K between H and G, we derive conditions under which enlarging the Lie algebra of K maintains nonnegative curvature on G/H. Such an enlarging is possible if (K,H) is a symmetric pair, which yields many new examples of nonnegatively curved homogeneous metrics. We provide other examples of spaces G/H with unexpectedly large families of nonnegatively curved homogeneous metrics.