Assume furthermore that $p=x_{0}$ and so the equivariant morphism $\varphi_{p,H}=\varphi_{H}\colon X_{\Sigma_{1}}\to X_{\Sigma_{2}}$ is a toric morphism. If ${\overline{L}}$ is a toric line bundle on $X_{\Sigma_{2}}$ equipped with the canonical metric, then $\varphi_{H}^{\ast}{\overline{L}}$ is a toric line bundle equipped with the canonical metric.