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On the Signature of the Ricci Curvature on Nilmanifolds

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 27 Jan 2022Embargo end date: 01 Jan 2020Publisher:Springer Science and Business Media LLCJournal:Transformation Groups, volume 29, pages 1-15 (issn: 1083-4362, eissn: 1531-586X,

Authors: Arroyo, Romina M.; Lafuente, Ramiro A.;

doi: 10.1007/s00031-021-09686-5 , 10.48550/arxiv.2009.11464

arXiv: http://arxiv.org/abs/2009.11464

On the Signature of the Ricci Curvature on Nilmanifolds

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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.

11 pages

Related Organizations

University of Queensland
Australia
National University of Córdoba
Argentina

Keywords

Mathematics - Differential Geometry, Differential Geometry (math.DG), FOS: Mathematics

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Funded by

ARC| Discovery Projects - Grant ID: DP180102185