The main result in this note is that the connection form with respect to frames in the orthonormal frame bundle for a left invariant Riemannian metric $g$ on $SU(2)$ becomes a YangMills connection if and only if $g$ is bi-invariant.
"Yang-Mills connections in orthonormal frame bundle over $SU(2)$." Tsukuba J. Math. 18 (1) 203 - 206, June 1994. https://doi.org/10.21099/tkbjm/1496162465