Positive Quaternion Kنhler 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 b 4 ( M ) = 1 . Generalising a result of Galicki and Salamon we prove that M 4 n in this case is homothetic to a quaternionic projective space if 2 ≠ n ⩽ 6 .