On the Signature of the Ricci Curvature on Nilmanifolds
Copyright policy )On the Signature of the Ricci Curvature on Nilmanifolds
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
Solvable, nilpotent (super)algebras, Mathematics - Differential Geometry, Ricci curvature, Differential geometry of homogeneous manifolds, Differential Geometry (math.DG), Nilpotent and solvable Lie groups, FOS: Mathematics, nilmanifolds
Solvable, nilpotent (super)algebras, Mathematics - Differential Geometry, Ricci curvature, Differential geometry of homogeneous manifolds, Differential Geometry (math.DG), Nilpotent and solvable Lie groups, FOS: Mathematics, nilmanifolds
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