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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 mathematics, a Hermitian symmetric space is a Kähler manifold M which, as a Riemannian manifold, is a Riemannian symmetric space. Equivalently, M is a Riemannian symmetric space with a parallel complex structure with respect to which the Riemannian metric is Hermitian. The complex structure is automatically preserved by the isometry group H of the metric, and so M is a homogeneous complex manifold. Some examples are complex vector spaces and complex projective spaces, with their usual Hermitian metrics and Fubini-Study metrics, and the complex unit balls with suitable metrics so that they become complete and Riemannian symmetric.