A Hermitian manifold is a complex manifold with a Hermitian metric on its holomorphic tangent space. Likewise, an almost Hermitian manifold is an almost complex manifold with a Hermitian metric on its holomorphic tangent space.
On a Hermitian manifold the metric can be written in local holomorphic coordinates (zα) as
where are the components of a positive-definite Hermitian matrix.
Read more about Hermitian Manifold: Riemannian Metric and Associated Form, Properties, Kähler Manifolds
Famous quotes containing the word manifold:
“There must be no cessation
Of motion, or of the noise of motion,
The renewal of noise
And manifold continuation....”
—Wallace Stevens (18791955)