Involutions fixing CPi(1) × HPi(n)

Let (M, T) be a closed manifold with an involution T. The fixed point set of T is F. In this article, bordism classes of the involutions with fixed point set F = CPi(1) × HPi(n) are determined, where CP(1) and HP(n) denote the 1-dimensional complex projective space and n-dimensional quaternionic projective space respectively, and n = 2p − 2 or n = 2p − 1 (p > 1).