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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V. del Barco is partially supported by FAEPEX-UNICAMP grant 2566/21 and FAPESP grant 2021/09197-8; V. del Barco and A. Moroianu are supported by MATHAMSUD Regional Program 21-MATH-06.
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del Barco, V., Moroianu, A. & Schichl, A. Weyl-Einstein structures on conformal solvmanifolds. Geom Dedicata 217, 9 (2023). https://doi.org/10.1007/s10711-022-00743-1
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DOI: https://doi.org/10.1007/s10711-022-00743-1