# Distribution

## Definition

Let be a connected differential manifold of dimension . A -dimensional **distribution** over is defined in the following equivalent ways:

- It is a section of the Grassmannian bundle of type
- It is a smooth association of, to each point in , a -dimensional subspace of the tangent space at the point. By
*smooth*here we mean that for every point, there is a neighbourhood where it can be generated by vector fields.