#### Vol. 298, No. 2, 2019

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Maximal symmetry and unimodular solvmanifolds

### Michael Jablonski

Vol. 298 (2019), No. 2, 417–427
##### 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 nonunimodular. 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.

##### Keywords
solvmanifold, solvable, Lie group, maximal symmetry, Ricci soliton, unimodular
##### Mathematical Subject Classification 2010
Primary: 22E25, 53C25, 53C30