On the signature of the Ricci curvature on nilmanifolds

2020/09/24 by Romina M. Arroyo, Arroyo, Romina M., Ramiro A. Lafuente +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.2009.11464

11 pages

arxiv created 2020/09/24 · arxiv updated 2020/09/25

Abstract

We completely describe the signatures of the Ricci curvature of left-invariant Riemannian metrics on arbitrary real nilpotent Lie groups. The main idea in the proof is to exploit a link between the kernel of the Ricci endomorphism and closed orbits in a certain representation of the general linear group, which we prove using the `real GIT' framework for the Ricci curvature of nilmanifolds.

Related

• The signature of the Ricci curvature of left-invariant Riemannian metrics on nilpotent Lie groups
• The signature of the Ricci curvature of left invariant Riemannian metrics on 4-dimensional Lie groups
• A canonical compatible metric for geometric structures on nilmanifolds
• The Ricci flow for simply connected nilmanifolds
• Invariants of complex structures on nilmanifolds