# Almost Hermitian manifold

From Diffgeom

*This article defines a differential manifold with the following additional structure -- the structure group is reduced to:* unitary group

## Contents

## Definition

An **almost Hermitian manifold** is the following data:

- A differential manifold
- A Riemannian metric on
- An almost complex structure viz a map such that with the further property that

Note that this gives a reduction of the structure group to the unitary group over complex numbers.