Let $R,S$ be Riemann surfaces and $f: R \to S$ an orientation preserving diffeomorphism. Then $f$ determines what is called a Beltrami differential denoted by $\mu \frac{d\bar{z}}{dz}$.
Local expression of $\mu$ is clear, however some texts mention that $\mu$ is a $(-1,1)$ form on $R$. What does that mean? More specifically is $\mu$ the section of a vector bundle, which one? Is there a coordinate free definition for $\mu$?