There are of course lots of definitions and references for this, but in the same way that, on a manifold $M$, * a Riemannian metric is a section of positive definite symmetric bilinear forms on $TM$ * or an almost complex structure is a section of $\textrm{End}(TM)$ which is everywhere * or an orientation is a non-vanishing section of $\Lambda^m TM$ is a spin structure, a section of quadratic forms $Q$ on $TM$ (of type $(s,t)$) and a vector bundle $S$ so that $\textrm{End}(S) \simeq \textrm{C}\ell(TM,Q)$? ...or something of the like? any references where it may be stated in this fashion?