A Simons type condition for instability of F-Yang-Mills connections

Abstract

F-Yang-Mills connections are critical points of F-Yang Mills functional on the space of connections of a principal fiber bundle, which are generalizations of Yang-Mills connections, p-Yang-Mills connections and exponential Yang-Mills connections and so on. Here, F is a strictly increasing $C^2$-function. In this paper, we extend Simons theorem for the instability of Yang-Mills connections to F-Yang-Mills connections. We derive a sufficient condition that any non-flat, F-Yang-Mills connection over submanifolds in a Euclidean space is unstable. In the standard sphere case, this condition is expressed by an inequality involving its dimension and the degree of the differential of the function F. Our main results are proved by extending Kobayashi-Ohnita-Takeuchi's calculation to F-Yang-Mills connections.