# Space of metrics on a bundle

From Diffgeom

## Definition

Let be a differential manifold and be a vector bundle. The **space of metrics** on is the set of all possible ways of giving the structure of a metric bundle.

This can be viewed as a subset of the space of sections of .

In the particular case where , we get the space of Riemannian metrics.

## Facts

### Gauge group acts on the space of metrics

The gauge group of the vector bundle acts on the space of metrics of .