Abstract
Let (M, g) be an n-dimensional (n ≥ 3) closed (compact and connected) Riemannian manifold. We obtain a necessary and sufficient condition for a projectively flat connection D with a Weyl structure (D, g, ω) in the tangent bundle TM over (M, g) to be a Yang-Mills connection. Moreover, we get the fact that the condition dω = 0 is a necessary and sufficient condition for the Ricci tensor RicD of a connection D with Weyl structure (D, g, ω) in the bundle TM over (M, g) to be symmetric, and then we get a necessary and sufficient condition for a projectively flat Einstein-Weyl connection D in the bundle TM over (M, g) to be a Yang-Mills connection.