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