On the signature of the Ricci curvature on nilmanifolds

Romina M. Arroyo; Ramiro A. Lafuente

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arXiv · 2009.11464

On the signature of the Ricci curvature on nilmanifolds

Romina M. Arroyo·Ramiro A. Lafuente

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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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Romina M. Arroyo, Ramiro A. Lafuente. 2020-09-24. On the signature of the Ricci curvature on nilmanifolds. https://arxiv.org/abs/2009.11464

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