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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In differential geometry, a quaternion-Kähler symmetric space or Wolf space is a quaternion-Kähler manifold which, as a Riemannian manifold, is a Riemannian symmetric space. Any quaternion-Kähler symmetric space with positive Ricci curvature is compact and simply connected, and is a Riemannian product of quaternion-Kähler symmetric spaces associated to compact simple Lie groups. For any compact simple Lie group G, there is a unique G/H obtained as a quotient of G by a subgroup.