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arXiv · 1803.06988

Maximal Symmetry and Unimodular Solvmanifolds

Michael Jablonski
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Abstract

Recently, it was shown that Einstein solvmanifolds have maximal symmetry in the sense that their isometry groups contain the isometry groups of any other left-invariant metric on the given Lie group. Such a solvable Lie group is necessarily non-unimodular. In this work we consider unimodular solvable Lie groups and prove that there is always some metric with maximal symmetry. Further, if the group at hand admits a Ricci soliton, then it is the isometry group of the Ricci soliton which is maximal.

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Michael Jablonski. 2018-03-19. Maximal Symmetry and Unimodular Solvmanifolds. https://doi.org/10.2140/pjm.2019.298.417

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