2024/11/19 by Yunhee Euh, Sinhwi Kim, Euh, Yunhee +5 · 1 citation
Mathematics · #17B30 #53C25 #53C30 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2411.12311
openalex publication_date 2024/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Riemannian manifold is called weakly Einstein if the tensor RiabcRj~~abc is a scalar multiple of the metric tensor gij. We consider weakly Einstein Lie groups with a left-invariant metric which are weakly Einstein. We prove that there exist no weakly Einstein non-abelian 2-step nilpotent Lie groups and no weakly Einstein non-abelian nilpotent Lie groups whose dimension is at most 5. We also prove that an almost abelian Lie group is weakly Einstein if and only if at the Lie algebra level it is defined by a normal operator whose square is a multiple of the identity.