  In this note we observe that on a 2-step nilpotent Lie group equipped with a
left-invariant SKT structure the (1,1)-part of the Bismut-Ricci form is
seminegative definite. As application we give a simplified proof of the
non-existence of invariant SKT static metrics on 2-step nilmanifolds and of the
existence of a long time solution to the pluriclosed flow in 2-step
nilmanifolds.
