A family of Yang-Mills connections on 4-dimensional pseudo-Riemannian spaces (Q1357695)

The author constructs Yang-Mills connections on some 4-dimensional pseudo-Riemannian spaces, namely: \(S^4\), \(S^1\times S^3\) and \(S^2\times S^2\), equipped with their indefinite canonical Riemannian metrics. Using a classical idea due to H.-C. Wang, the connections come from the lifting of appropriate Lie group actions on the base spaces to some bundles. It can be shown that these canonical connections satisfy the Yang-Mills equations. The value of the Yang-Mills functional as well as the index and nullity of their second variations are computed for these connections.