Weyl-Einstein structures on conformal solvmanifolds

A conformal Lie group is a manifold $(M,c)$ such that $M$ has structure and $c$ the defined by left-invariant metric $g$ on $M$. We study Weyl-Einstein structures solvable groups their compact quotients. In case, we show every solvmanifold carrying Einstein. also there are no non-abelian nilpotent groups, classify them in almost abelian case. Furthermore, determine precise list (up to automorphisms) of metrics simply connected dimension 3 structures.