2008/04/23 by Schwachhofer, Lorenz, Tapp, Kristopher
#53Cxx #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.0804.3729
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.