  Let $(M^n,g)$ be an $n$-dimensional compact connected Riemannian manifold
with smooth boundary. We show that the presence of a nontrivial conformal
gradient vector field on $M$, with an appropriate control on the Ricci
curvature makes $M$ to be isometric to a hemisphere of $\mathbb{S}^{n}$. We
also prove that if an Einstein manifold admits nonzero conformal gradient
vector field, then its scalar curvature is positive and it is isometric to a
hemisphere of $\mathbb{S}^{n}$. Furthermore, we prove that if $ M $ admits a
nontrivial conformal vector field and has constant scalar curvature, then the
scalar curvature is positive. Finally, a suitable control on the energy of a
conformal vector field implies that $M$ is isometric to a hemisphere
$\mathbb{S}^n_+$.
