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On solvable Lie groups of negative Ricci curvature

Abstract

We study solvable Lie groups which admit a left-invariant metric of strictly negative Ricci curvature. We obtain necessary and sufficient conditions of the existence of such a metric for Lie groups the nilradical of whose Lie algebra is either abelian or Heisenberg or standard filiform and discuss some open questions.

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Correspondence to Y. Nikolayevsky.

Additional information

The first author is partially supported by ARC Discovery Grant DP130103485. The second author is supported in part by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-921.2012.1) and by Federal Target Grant “Scientific and educational personnel of innovative Russia” for 2009–2013 (Agreement No. 8206, Application No. 2012-1.1-12-000-1003-014).

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Nikolayevsky, Y., Nikonorov, Y.G. On solvable Lie groups of negative Ricci curvature. Math. Z. 280, 1–16 (2015). https://doi.org/10.1007/s00209-015-1410-2

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  • DOI: https://doi.org/10.1007/s00209-015-1410-2

Keywords

  • Solvable Lie algebra
  • Nilradical
  • Negative Ricci curvature

Mathematics Subject Classification

  • 53C30
  • 22E25