# Almost complex manifold

From Diffgeom

*This article defines a differential manifold with the following additional structure -- the structure group is reduced to:* general linear group over complex numbers

## Contents

## Definition

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

- A differential manifold
- At each point, a complex structure to the vector space at that point. In other words, for every point, we give a linear map such that , with varying smoothly with the point.

## Relation with other structures

### Stronger structures

### Weaker structures

- Almost symplectic manifold:
`Further information: Almost complex structure gives symplectic form` - Oriented manifold