On Ricci negative derivations
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María Valeria Gutiérrez
Abstract
Given a nilpotent Lie algebra, we study the space of all diagonalizable derivations such that the corresponding one-dimensional solvable extension admits a left-invariant metric with negative Ricci curvature. Lauret and Will have conjectured that such a space coincides with an open and convex subset of derivations defined in terms of the moment map for the variety of nilpotent Lie algebras. We prove the validity of the conjecture in dimensions ≤ 5, as well as for Heisenberg Lie algebras and standard filiform Lie algebras.
Acknowledgement
I would like to thank to my PhD advisor Dr. Jorge Lauret for his continued guidance during the preparation of this paper.
Funding: Partially supported by a CONICET doctoral fellowship and a Consejo Interuniversitario Nacional fellowship.
Communicated by: T. Grundhöfer
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Semistable Higgs bundles on elliptic surfaces
- On the rigidity of harmonic-Ricci solitons
- On Ricci negative derivations
- Approximating coarse Ricci curvature on submanifolds of Euclidean space
- Convex cones spanned by regular polytopes
- On the geography of line arrangements
- Towards resolving Keller’s cube tiling conjecture in dimension seven
Artikel in diesem Heft
- Frontmatter
- Semistable Higgs bundles on elliptic surfaces
- On the rigidity of harmonic-Ricci solitons
- On Ricci negative derivations
- Approximating coarse Ricci curvature on submanifolds of Euclidean space
- Convex cones spanned by regular polytopes
- On the geography of line arrangements
- Towards resolving Keller’s cube tiling conjecture in dimension seven
