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

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We show that any left invariant metric with harmonic curvature on a solvable Lie group is Ricciparallel. We show the same result for any Lie group of dimension ≤ 6. Click to show full abstract

We show that any left invariant metric with harmonic curvature on a solvable Lie group is Ricciparallel. We show the same result for any Lie group of dimension ≤ 6.

Keywords: lie; left invariant; lie groups; solvable lie; harmonic curvature

Journal Title: Journal of Geometry and Physics
Year Published: 2022

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