Symmetries, tensors, and the Horrocks bundle.

A study of tensors on the quaternionic projective plane HP 2 arising from a stable 3-form on C 6 and an associated action of SU (3) is related to the existence of a holomorphic rank 3 vector bundle over CP 5 discovered by Horrocks. It also leads to the construction of SU (3) invariant Spin (7) structures on HP 2 , which are characterised in terms of associated 4-forms. [ABSTRACT FROM AUTHOR]