ON INSTABILITY OF F-YANG-MILLS CONNECTIONS OVER IRREDUCIBLE SYMMETRIC R-SPACES

The notion of F-Yang-Mills connections gives a generalization of Yang-Mills connections, p-Yang-Mills connections and exponential Yang-Mills connections. Here, F is a strictly increasing C²-function. In this paper, we study an instability for F-Yang-Mills connections on principal fiber bundles over irreducible symmetric R-spaces. In classical Yang-Mills theory, Simons showed that the non-existence theorem for non-flat, weakly stable Yang-Mills connections over the standard sphere with dimension more than four. Recently, a Simons type instability theorem for F-Yang-Mills connections over the standard sphere was given by BabaShintani. The purpose of this paper is to prove that the converse of this theorem does not hold in general. In fact, we give a concrete example of F-Yang-Mills instable, irreducible symmetric R-spaces except for the standard sphere. For this, we first give a sufficient condition for an irreducible symmetric R-space to be F-Yang-Mills instable. Next, by classifying the irreducible symmetric R-spaces satisfying this condition, we find that the standard sphere and the Cayley projective plane are only such irreducible symmetric R-spaces. In particular, the Cayley projective plane is F-Yang-Mills instable.