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Mathematics > Differential Geometry

Title: Maximal Symmetry and Unimodular Solvmanifolds

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.
Comments: 9 pages
Subjects: Differential Geometry (math.DG)
Cite as: arXiv:1803.06988 [math.DG]
  (or arXiv:1803.06988v1 [math.DG] for this version)

Submission history

From: Michael Jablonski [view email]
[v1] Mon, 19 Mar 2018 15:26:47 GMT (10kb)