Solvable extensions of negative Ricci curvature of filiform Lie groups

2015/01/09 by Yuri Nikolayevsky, Nikolayevsky, Y.
Mathematics · Physics and Astronomy · #22E25 #53C30 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1501.02028

openalex publication_date 2015/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give necessary and sufficient conditions of the existence of a left-invariant metric of strictly negative Ricci curvature on a solvable Lie group the nilradical of whose Lie algebra \mathfrakg is a filiform Lie algebra \mathfrakn. It turns out that such a metric always exists, except for in the two cases, when \mathfrakn is one of the algebras of rank two, L_n or Q_n, and \mathfrakg is a one-dimensional extension of \mathfrakn, in which cases the conditions are given in terms of certain linear inequalities for the eigenvalues of the extension derivation.

Citations

• Curvatures of left invariant metrics on lie groups

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