Strongly solvable spaces (Q2263803)

This paper is devoted to the study of the actions by isometries on solvmanifolds. The author proves that the isometry group is linear for an admissible completely solvable Lie group equipped with a left-invariant metric. Moreover a procedure for getting this isometry group is given. Equivalent conditions for the existence of compact quotients are found, once we start with a simply connected almost completely solvable positive Lie group \(S\) equipped with a left invariant metric \(g\): \(S\) is unimodular; \((S,g)\) is symmetric. Examples arise from solvable Lie groups admitting an Einstein metric. The paper is very clear, well motivated and advances and relations towards the proof of the Alekseevsky conjecture are shown.