ON THE INFINITESIMAL AUTOMORPHISM OF QUATERNIONIC STRUCTURES

We consider the following four Lie groups: GL(n, H), Sp(n), GL(n, H) S p(1), Sp(n) Sp(1), and the corresponding G-structures on 4n-dimensiona l manifolds M. We study their infinitesimal automorphisms xi and the r elations between them, in particular when M is a hyperkahler or a quat ernion Kahler manifold. We obtain the vanishing of all the infinitesim al automorphisms on compact quaternion Kahler manifolds with negative scalar curvature, and a formula relating the zeroes of xi with the cha racteristic numbers of M in the positive scalar curvature case.