Hermitian symmetric space

Summary

A Hermitian symmetric space is a symmetric space with a compatible complex structure, for which every geodesic symmetry is holomorphic. Examples are the complex projective spaces, the Grassmannians, the unit disc and the Siegel upper half space. Such a space is automatically a Kähler manifold. The irreducible ones of noncompact type are bounded symmetric domains in $\C^n$, and they are the home of automorphic forms in several variables.