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Homogeneous Metrics with Nonnegative Curvature

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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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Authors and Affiliations

  1. Fakultät für Mathematik, Technische Universität Dortmund, Vogelpothsweg 87, 44221, Dortmund, Germany

    Lorenz Schwachhöfer

  2. Department of Mathematics, Saint Joseph University, 5600 City Avenue, Philadelphia, PA, 19131, USA

    Kristopher Tapp

Authors
  1. Lorenz Schwachhöfer
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  2. Kristopher Tapp
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Correspondence to Lorenz Schwachhöfer.

Additional information

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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