On Ricci negative derivations
Differential Geometry
2020-12-07 v1
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. It has been conjectured by Lauret-Will 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 dimension 5, as well as for Heisenberg and standard filiform Lie algebras.
Cite
@article{arxiv.2012.02597,
title = {On Ricci negative derivations},
author = {Valeria Gutiérrez},
journal= {arXiv preprint arXiv:2012.02597},
year = {2020}
}
Comments
19 pages, 8 figures. arXiv admin note: text overlap with arXiv:1912.06204 by other authors