# Isometry-invariant fibration

From Diffgeom

Template:Isometry-invariance property

## Definition

### Symbol-free definition

Given a manifold with a compatible Riemannian metric, a fibration from the manifold is said to be **isometry-invariant** if any isometry of the Riemannian manifold permutes the fibres of the fibration (viz preserves the equivalence relation of being in the same fibre).