  The main objective of this paper is to investigate the $m$-quasi Einstein
manifold when the potential function becomes convex. In this article, it is
proved that an $m$-quasi Einstein manifold satisfying some integral conditions
with vanishing Ricci curvature along the direction of potential vector field
has constant scalar curvature and hence the manifold turns out to be an
Einstein manifold. It is also shown that in an $m$-quasi Einstein manifold the
potential function agrees with Hodge-de Rham potential up to a constant.
Finally, it is proved that if a complete non-compact and non-expanding
$m$-quasi Einstein manifold has bounded scalar curvature and the potential
vector field has global finite norm, then the scalar curvature vanishes.
