TITLE: Compact quaternionic Kahler manifolds of negative curvature: examples
QUESTION [12 upvotes]: There is a well known problem of LeBrun-Salamon:
are there any non-symmetric compact quaternionic-Kahler
manifolds of positive scalar (and Ricci) curvature?
It is hard and still unsolved:
Quaternionic-Kahler metrics whose universal covers have only discrete isometry groups?
The symmetric compact quaternionic-Kahler manifolds
("Wolf spaces") are understood and classified. However,
for each Wolf space there is the dual symmetric
space, say, $G/H$, which is quaternionic-Kahler
of negative scalar (and Ricci) curvature.
For any lattice $\Gamma\subset G$,
the double quotient $\Gamma\backslash G/H$
is a locally symmetric quaternionionic-Kahler
orbifold of negative curvature and finite volume.
However, it can have cusp points, and then it 
is non-compact.
Are there any compact locally symmetric
quaternionionic-Kahler orbifolds? Manifolds?
I could not find a reference to either existence
or non-existence results.

REPLY [8 votes]: Any (Riemannian) symmetric space admits a cocompact lattice. This is due to A. Borel, Compact Clifford-Klein forms of symmetric spaces, Topology 2,  1963, pp.111-122. The quaternionic hyperbolic space is symmetric and quaternionic-Kahler.