We denote by $\widehat{\rm Pic}(X)$ the group of isomorphism classes of line bundles on $X$ equipped with a model metric. There is a well defined injective map $c_{1}:\widehat{\rm Pic}(X)\to\mathcal{Z}^{1,1}(X)$ which sends the class of $(L,\|\ \|_{\mathscr{L}})$ to the class of ${\mathscr{L}}$. We denote its image by $c_{1}(L,\|\ \|_{\mathscr{L}})$ and call it the curvature form of $(L,\|\ \|_{\mathscr{L}})$.