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Mathematische Zeitschrift

, Volume 280, Issue 1–2, pp 1–16 | Cite as

On solvable Lie groups of negative Ricci curvature

  • Y. Nikolayevsky
  • Yu. G. Nikonorov
Article

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.

Keywords

Solvable Lie algebra Nilradical Negative Ricci curvature 

Mathematics Subject Classification

53C30 22E25 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsLa Trobe UniversityMelbourneAustralia
  2. 2.South Mathematical Institute of VSC RASVladikavkazRussia

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