Let $(M^2,g)$ and $(\bar{M},\bar{g})$ be two Riemannian manifolds. Suppose that $\mathcal{W}$ is the Willmore functional on the set of immersion functions from $M^2$ to $\bar{M}$.

We know that $(\bar{M},\bar{g})$ is supposed to be of constant sectional curvature at every paper where the critical points of Willmore functional have been investigated. My question is: may I suppose $(\bar{M},\bar{g})$ to be any Riemannian manifold?