In a previous paper we proved a lower bound for the spectrum of the Dirac
operator on quaternionic Kaehler manifolds. In the present article we show that
the only manifolds in the limit case, i.e. the only manifolds where the lower
bound is attained as an eigenvalue, are the quaternionic projective spaces. We
use the equivalent formulation in terms of the quaternionic Killing equation
and show that a nontrivial solution defines a parallel spinor on the associated
hyperkaehler manifold.Comment: 19 pages, LaTeX2e, fullpage styl