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

Authors :
Aberaouze, Ilyes
Boucetta, Mohamed
Publication Year :
2021

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.<br />Comment: 17 pages

Subjects

Subjects :
Mathematics - Differential Geometry
22E15, 53C20, 22E25

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2108.06512
Document Type :
Working Paper
Full Text :
https://doi.org/10.1016/j.geomphys.2022.104517
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