REMARKS ON A TRIPLE OF K-CONTACT STRUCTURES

Abstract

We show that any K-contact 3-structure on a 7-dimensional Riemannian manifold is a Sasakian 3-structure. By this we see that Konishi's construction of a 3-Sasakian manifold over a quaternionic Kähler manifold works for dimension≥4. We also study the case of quaternionic Kähler manifolds of negative scalar curvature by defining a triple of K-contact structures of nS-type.