Hermitian symmetric space

A Hermitian symmetric space is a type of Riemannian manifold that possesses a certain symmetric structure along with a compatible complex structure. More specifically, a Hermitian symmetric space is defined as a homogeneous space \( G/K \) where: 1. **Complex Structure**: The space has a complex manifold structure, meaning it can be described using complex coordinates, and it possesses a compatible Hermitian metric \( g \).