Solvable Lie groups of negative Ricci curvature

Abstract

We consider the question of whether a given solvable Lie group admits a left-invariant metric of strictly negative Ricci curvature. We give necessary and sufficient conditions of the existence of such a metric for the Lie groups the nilradical of whose Lie algebra is either abelian or Heisenberg or standard filiform, and discuss some open questions.

18 pages

Cited by in corpus (4)

• Geometric flows and their solitons on homogeneous spaces
• Non-solvable Lie groups with negative Ricci curvature
• On Ricci negative derivations
• Negative Ricci curvature on some non-solvable Lie groups II