Bach-flat Lie groups in dimension 4
Elsa Abbena, Sergio Garbiero, Simon Salamon
TL;DR
This paper demonstrates the existence of 4-dimensional solvable Lie groups with left-invariant metrics that have zero Bach tensor but are neither conformally Einstein nor half conformally flat, expanding understanding of Bach-flat geometries.
Contribution
It constructs explicit examples of 4D solvable Lie groups with Bach-flat metrics that are not conformally Einstein or half conformally flat, revealing new geometric structures.
Findings
Existence of 4D solvable Lie groups with Bach-flat metrics
Examples are neither conformally Einstein nor half conformally flat
Advances classification of Bach-flat geometries in low dimensions
Abstract
We establish the existence of solvable Lie groups of dimension 4 and left-invariant Riemannian metrics with zero Bach tensor which are neither conformally Einstein nor half conformally flat.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds