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arXiv · 2108.06512

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

Ilyes Aberaouze·Mohamed Boucetta
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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.

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Ilyes Aberaouze, Mohamed Boucetta. 2021-08-14. Left invariant Riemannian metrics with harmonic curvature are Ricci-parallel in solvable Lie groups and Lie groups of dimension $\leq6$. https://doi.org/10.1016/j.geomphys.2022.104517

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