Left invariant Riemannian metrics with harmonic curvature are Ricci-parallel in solvable Lie groups and Lie groups of dimension $\leq6$

Ilyes Aberaouze; Mohamed Boucetta

doi:10.1016/j.geomphys.2022.104517

paper

Left invariant Riemannian metrics with harmonic curvature are Ricci-parallel in solvable Lie groups and Lie groups of dimension $\leq 6$

arXiv:2108.06512 · doi:10.1016/j.geomphys.2022.104517

Abstract

We show that any left invariant metric with harmonic curvature on a solvable Lie group is Ricci-parallel. We show the same result for any Lie group of dimension $\leq$ 6.

arXiv comment17 pages

Left invariant Riemannian metrics with harmonic curvature are Ricci-parallel in solvable Lie groups and Lie groups of dimension ≤6

Abstract

Left invariant Riemannian metrics with harmonic curvature are Ricci-parallel in solvable Lie groups and Lie groups of dimension $\leq 6$