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arXiv · 2203.13642

Weyl-Einstein structures on conformal solvmanifolds

Viviana del Barco·Andrei Moroianu·Arthur Schichl
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Abstract

A conformal Lie group is a conformal manifold $(M,c)$ such that $M$ has a Lie group structure and $c$ is the conformal structure defined by a left-invariant metric $g$ on $M$. We study Weyl-Einstein structures on conformal solvable Lie groups and on their compact quotients. In the compact case, we show that every conformal solvmanifold carrying a Weyl-Einstein structure is Einstein. We also show that there are no left-invariant Weyl-Einstein structures on non-abelian nilpotent conformal Lie groups, and classify them on conformal solvable Lie groups in the almost abelian case. Furthermore, we determine the precise list (up to automorphisms) of left-invariant metrics on simply connected solvable Lie groups of dimension 3 carrying left-invariant Weyl-Einstein structures.

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Viviana del Barco, Andrei Moroianu, Arthur Schichl. 2022-03-25. Weyl-Einstein structures on conformal solvmanifolds. https://doi.org/10.1007/s10711-022-00743-1

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