in the present context
In the physical context already referred to, $K$ is the density of ...... [Note the double r in referred.]
Berg spaces have been rarely considered outside the metric context.
The context will make it clear whether $S$ denotes a permutation of $M$ or the corresponding symmetry.
When the target space is clear from context, we just write ......
If $G$ is clear from context, then we suppress reference to it in the notation.
Strictly speaking, we should write something like $a(l,m,n)$ to reflect the dependence; we shall rely upon context instead.
To place Theorem 1 in context, consider two real vector fields ......