A Nearly Quaternionic Structure on SU(3).

link: http://arxiv.org/abs/0908.4183
Abstract

It is shown that the compact Lie group SU(3) admits an Sp(2)Sp(1)-structure
whose distinguished 2-forms $\omega_1,\omega_2,\omega_3$ span a differential
ideal. This is achieved by first reducing the structure further to a subgroup
isomorphic to SO(3).