Yang–Mills equations in 4-dimensional conform connection manifolds

In this article on the simplest examples of compact 4-dimensional conform connection manifolds (real quadrics in 5-dimensional projective space) we show that the only invariant, quadratic relatively to the curvature $\Phi$ of the connection, is Yang–Mills functional $\int\vert\operatorname{tr}(\ast\Phi\wedge\Phi)\vert$. The author of the article doesn't know, whether 4-form $\vert\operatorname{tr}(\ast\Phi\wedge\Phi)\vert$ is invariant in any 4-dimensional conform connection manifold.