On the signature of the Ricci curvature on nilmanifolds
Romina M. Arroyo, Ramiro A. Lafuente

TL;DR
This paper characterizes the possible signatures of Ricci curvature for left-invariant metrics on all real nilpotent Lie groups, using a novel approach linking Ricci kernel properties to group actions.
Contribution
It provides a complete description of Ricci curvature signatures on nilmanifolds by connecting geometric properties to representation theory via real GIT.
Findings
Complete classification of Ricci signatures on nilpotent Lie groups
Establishment of a link between Ricci kernel and group orbits
Application of real GIT to Ricci curvature analysis
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.
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