Abstract
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.
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Communicated by Carolyn Gordon.
L. Schwachhöfer was supported by the Schwerpunktprogramm Differentialgeometrie of the Deutsche Forschungsgesellschaft.
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Schwachhöfer, L., Tapp, K. Homogeneous Metrics with Nonnegative Curvature. J Geom Anal 19, 929–943 (2009). https://doi.org/10.1007/s12220-009-9081-z
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DOI: https://doi.org/10.1007/s12220-009-9081-z