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In this paper, we define the corresponding submanifolds to left-invariantRiemannian metrics on Lie groups, and study the following question: does adistinguished left-invariant Riemannian metric on a Lie group correspond to adistinguished submanifold? As a result, we prove that the solvsolitons onthree-dimensional simply-connected solvable Lie groups are completelycharacterized by the minimality of the corresponding submanifolds.

Three-dimensional solvsolitons and the minimality of the corresponding submanifolds