Positive Quaternion Kähler Manifolds with fourth Betti number equal to one

Positive Quaternion Kähler Manifolds are Riemannian manifolds with holonomy contained in Sp(n)Sp(1) and with positive scalar curvature. Conjecturally, they are symmetric spaces. In this article we are mainly concerned with Positive Quaternion Kähler Manifolds M satisfying b4(M)=1. Generalising a result of Galicki and Salamon we prove that M4n in this case is homothetic to a quaternionic projective space if 2≠n⩽6.