A Wolf space is a compact, simply connected, irreducible quaternion-Kähler symmetric space
of positive dimension. Equivalently, it is a homogeneous
space
whose isotropy group has a distinguished factor locally
isomorphic to
and whose holonomy is contained in .
The quaternionic projective spaces are Wolf spaces. Additional examples arise from each compact simple Lie group and include quaternionic
Grassmannians and exceptional homogeneous
spaces.
Besse, A. L. Einstein Manifolds. Berlin, Germany: Springer-Verlag, 1987.Hu, Z.; Liu,
K.; and Wan, X. "Transverse Rational Curves and the LeBrun-Salamon Conjecture."
7 Oct 2026. https://arxiv.org/abs/2610.10410.Wolf,
J. A. "Complex Homogeneous Contact Manifolds and Quaternionic Symmetric
Spaces." J. Math. Mech.14, 1033-1047, 1965.
whose isotropy group has a distinguished factor locally
isomorphic to 
and whose holonomy is contained in 
.
