A Hermitian manifold is a type of complex manifold equipped with a Riemannian metric that is compatible with the complex structure. More formally, a Hermitian manifold consists of the following components: 1. **Complex Manifold**: A manifold \( M \) that is equipped with an atlas of charts where the transition functions are holomorphic mappings. This means that the local coordinates can be expressed in terms of complex variables.
Articles by others on the same topic
A Hermitian manifold is a complex manifold whose tangent bundle carries a smoothly varying positive-definite Hermitian form. Its real part is a Riemannian metric invariant under the complex structure .