THE CONJUGATE CONNECTION OF A YANG-MILLS CONNECTION

Abstract

In general, the properties of a given connection and the conjugate connection in a vector bundle E over a closed Riemannian manifold (M, g) are different. It is interesting to find whether or not the conjugate connection of a Yang-Mills connection in a vector bundle E over (M, g) is a Yang-Mills connection. In this paper, we get the fact that a connection D in a vector bundle E over (M, g) is a Yang-Mills connection if and only if the conjugate connection is a Yang-Mills connection.