Classification of SNC-algebras in dimension five
Differential Geometry
2026-05-08 v2
Abstract
Every homogeneous manifold of negative curvature is known to be isometric to a Lie group with a left invariant metric. We define an SNC-algebra to be a Lie algebra which admits an inner product of strictly negative curvature. In the author's joint paper in 2022, we classified SNC-algebras in dimension four. In this article, we classify SNC-algebras in dimension five, as well as we calculate Ricci curvature of SNC-algebras in dimension four.
Cite
@article{arxiv.2604.24593,
title = {Classification of SNC-algebras in dimension five},
author = {Haruka Sugai},
journal= {arXiv preprint arXiv:2604.24593},
year = {2026}
}
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32 pages