2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61657We describe an action of $U(1)\times Sp(1)$ on $HP^7$ that allows to obtain a $Z_2$-quotient of CAYLEY (the Grassmannian of oriented 4-planes in $R^8$ closed under the three-fold cross product) by quaternionic Kähler reduction.To appear in: Proceedings of the International Congress of Differential Geometry in the memory of A. Gray, held in Bilbao, Sept. 2000; Contemp. Math., AMS 2001Differential Geometrytext