ON EXPONENTIAL YANG-MILLS CONNECTIONS

In this paper, we study a new functional, i.e., the exponential Yang-Mills functional Y M(e) on the space of all smooth connections del of a vector bundle E over a compact Riemannian manifold (M, g) which is defined by Y M(e)(del) = integral(M) exp(1/2\\R(del)\\(2))upsilon(g), where \\R(del)\\ is the curvature tenser of a connection del. A critical point of Y M(c) is called an exponential Yang-Mills connection. If \\R(del)\\ is constant, a smooth connection del is an exponential Yang-Mills connection if it is a Yang-Mills one. We show for any vector bundle E, that the functional Y M(e) admits a minimising connection del which is C(a)lpha-Holder continuous for all 0 < alpha < 1. We show the existence theorem of a smooth exponential Yang-Mills connection and study its properties and the second variation formula.