  We prove that there do not exist odd-dimensional stable compact minimal
immersions in the product of two complex projective spaces. We also prove that
the only stable compact minimal immersions in the product of a quaternionic
projective space with any other Riemannian manifold are the products of
quaternionic projective subspaces with compact stable minimal immersions of the
second manifold in the Riemmanian product. These generalize similar results of
the second-named author of immersions with low dimensions or codimensions to
immersions with arbitrary dimensions. In addition, we prove that the only
stable compact minimal immersions in the product of a octonionic projective
plane with any other Riemannian manifold are the products of octonionic
projective subspaces with compact stable minimal immersions of the second
manifold in the Riemmanian product.
