I am reading the paper Minimal surfaces of constant curvature in $S^n$, wrote by Professor Robert Bryant in 1985. In this paper, the author introduced some operators to give a new method in order to classify the minimal surfaces of constant ($>0$, $<0$ or $=0$) curvature in $\mathbb{S}^n$.
In section 1, the author gave the definitions of the 3 operators after introducing a complex line bundle, where I can hardly understand.
Question 1: In page 261, what is a "complex line bundle of $1$-forms"? I mean, what are the total space and the fibre of this bundle? Also, why the complex line bundle can be the multiples of a $1$-form $\omega$ since these two concepts are totally different?
Question 2: In the line 6 in the page 261, why any section $\sigma$ of $\tau^m$ can be write as $$\sigma=s(\omega)^m$$ for a unique function $s$ on the bundle of oriented orthonormal frames?
Question 3: In the line 7 in the page 261, why we have $$ds=-mi\rho s+s'\omega+s''\bar{\omega}?$$
I would be very grateful if anyone could help me!