Positive quaternionic Kahler manifolds and symmetry rank

A quaternionic Kahler manifold M is called positive if it has positive scalar curvature. The main purpose of this paper is to prove several connectedness theorems for quaternionic immersions in a quaternionic Kahler manifold, e.g. the Barth-Lefschetz type connectedness theorem for quaternionic submanifolds in a positive quaternionic Kahler manifold. As applications we prove that, among others, a 4m-dimensional positive quaternionic Kahler manifold with symmetry rank at least (m - 2) must be either isometric to HPm or Gr(2)(Cm+2), if m greater than or equal to 10.