In a paper I've found a repeated notation with differential forms and, since I have never seen it before, my question is if there is a misprint or if it is an operation I don't know.
I have a smooth manifold $M$ and a $1-$form $\alpha\in\Lambda^1(M)$. Then for a function $g\in\mathcal{C}^{\infty}(M)$ they define $g.\alpha$
Is there a meaning for this notation? I assume it means rescaling $\alpha$ by $g$ but usually this reads $g\alpha$
In fact, the bundle $\Lambda M$ is a $\mathcal{C}^{\infty}(M)$ module : you can do linear combinations of differential forms with functions as coefficients. In your example, if $\alpha$ is a $1$-form and $g$ a smooth map, if $p\in M$ and $X$ is a vector field, then $(g\cdot \alpha)(X_p) = g(p)\alpha_p(X_p)$